Chapter 5 - MAGNETISM AND MATTER
Magnetism
Magnetism in Physics is defined as the property of the material that is responsible for the magnetic behaviour of the magnets. Magnetism is defined as the force that is produced by the moving charge and it attracts or repels other magnets and moving charge. Initially, magnetism is defined as the property of some material to attract or repel some other magnets. Later it was discovered that all the moving charges are considered to be magnets and their property of attraction or repulsion is called magnetism.
Here, in this article, we will learn about, Magnetism Definition, History of Magnets, Causes of Magnetism, Magnetic Materials, Properties of Magnets and others in detail.
Table of Content
What is Magnetism?
Magnetism is a phenomenon induced by the force exerted by magnets, which produces fields that attract or repel other metallic objects. It occurs as a result of electrically charged particles. A magnetic field exerts a force on other metallic objects called the Lorentz force this force depends on the strength of the magnetic field and the velocity of the charged particle. For any magnets.
- Like poles repel each other.
- Opposite poles attract each other.
Magnetism Definition
Magnetism in general is defined as the phenomenon associated with the magnetic fields. We know that magnetic fields are produced by moving electric charges and thus magnetism is the property of the moving charged particle that produces a force that is exerted on the other metallic material inside the magnetic field of the moving charge.
History Of Magnetism
Everything around us is made up of electrons and they are continuously moving. So one might ask why everything around us is not a magnet including ourselves. The answer to this is, that individual electrons moving around any object behave as a magnet but overall all these small magnets cancel out each other’s magnetic property and thus not all material behaves as a magnet.
In some materials, all the electrons are arranged in such a way that they do not cancel each other and they are called ferromagnetic material. These ferromagnetic materials are called permanent magnets as they attract other metallic materials naturally. The property of magnetism is first observed in a material called Magnetite(Fe3O4) hence the name magnets. These magnetite is scattered all around the Earth’s crust and was first noticed by a shepherd in Greece.
Magnetism Properties
The various properties of the magnets are,
Attractive Property: Magnets attracts other ferromagnetic and paramagnetic substances.
Repulsive Property: Like poles of a magnets always repel each other.
Magnetism of Earth
Earth have a magnetic field and this is observed whenever we pin a compass it always arranged in the north south direction this is because of the Earth magnetism. Geographical North Pole of the Earth is the magnetic South Pole of the Earth and geographical South pole of the Earth is the magnetic North pole of the Earth.
What is Magnetic Field?
Magnetic field or magnetism field is defined as the space or region around a magnet in which magnetic force is applied to another metallic material.
The magnetic field or magnetism can be represented in a variety of ways. It may be represented mathematically as a vector field that can be displayed as various sets on a grid. Another method is to utilize field lines. Magnetic field lines never cross one other. The denser the magnetism field lines the more strength of the magnetic field they represent. The magnetic field of the bar magnet is shown in the image added below,
Unit of Magnetic Field
Magnetic field is measured by determining the intensity and direction of the magnetic field. The measurement is required because each magnetic field differs from the others. In a magnetic field, we measure two things that are,
- Magnetic Field Strength(H) is measured in Ampere/meter.
- Magnetic Flux Density(B) measured in Tesla.
Magnetic Field Lines
Magnetic field lines are a type of visual representation of magnetic fields. They describe the magnetic force direction and magnetic force strength at any particular point near the magnet.
The magnitude of the field is indicated by the density of the lines. For example, at the poles of a magnet, the magnetic field is stronger and denser. It becomes weaker as we go away from the poles, and the lines become less dense.
Magnetic Field Line Properties
There are various properties of the magnetic field lines and some of them are,
- Magnetic field lines never cross one other.
- Magnetic field lines are always closed loops.
- The density of the field lines reflects the field’s intensity.
- Magnetic field lines always arise from or begin at the north pole and end at the south pole.
Magnetic Materials
All the materials around us can be categorized into three types that are,
- Diamagnetic Materials
- Paramagnetic Material
- Ferromagnetic Materials
Diamagnetic Material: In general most of the materials around us have diamagnetism. In this material, they have paid electrons and thus they have no magnetic property. Examples of Diamagnetic Materials are Copper, Gold, Silver, etc.
Paramagnetic Materials: The materials that have unpaired electrons are called paramagnetic materials and they show paramagnetism, i.e. they experience some force inside the magnetic field of other magnets. The magnetic moment of the electrons does not align in the case of the paramagnetic materials. Examples of Paramagnetic materials are Magnesium, Lithium, etc.
Ferromagnetic Materials: There are very few materials that have ferromagnetism and they can be made permanent magnets. In ferromagnetic materials they have unpaired electrons and their magnetic moment is free to align itself freely. Examples of Ferromagnetic materials are, Iron, Cobalt, and Nickel.
Magnetism Types
There are five types of magnetism that are,
- Diamagnetism
- Paramagnetism
- Ferromagnetism
- Anti-Ferromagnetism
- Ferrimagnetism
Diamagnetism
Diamagnetism is the property of the Diamagnetic Materials. These materials have paired electrons and they do not experience force in magnetic field. In a diamagnetic substance there are no permanent magnetic dipole moment of the electron.
Paramagnetism
Paramagnetism is the property of the material that have unpaired of the electrons. These material are called the paramagnetic material. Here in these material there are magnetic moment of the electrons and they tends to be arranged randomly such that there overall magnetic moment cancel out each other.
Ferromagnetism
Magnetism of the ferromagnetic material is called the ferromagnetism. These materials have the tendency to to arrange themselves in the influence of an external magnetic field and thus increase magnetic moment of the material.
Anti-Ferromagnetism
Anti-ferromagnetism is the property of the material in which the individual magnetic moment of the material arranges itself such that its magnitude is the same with its adjacent one but the direction is opposite, which cancels the overall magnetism of the material.
Ferrimagnetism
Ferrimagnetism is the property of the material in which the adjacent magnetic moment of the electrons are opposite to each other and their magnitude is not the same. thus, the material shows the overall magnetism and experiences some force in the external magnetic field.
Magnetic Force
The magnetic force is the attraction or repulsion force that exists between electrically charged particles as a result of their motion.
The magnetic force between two moving charges is defined as the force imposed on one’s charge by the magnetic field generated by the other. This force is responsible for magnets attracting or repelling one another.
A compass, a motor, the magnets that keep things on the refrigerator, railway lines, and new roller coasters are all examples of magnetic force. A magnetic field is created by all moving charges, and the charges that travel across its areas experience a force. Depending on whether the force is attractive or repulsive, it might be positive or negative. The magnetic force of an item is determined by its charge, velocity, and magnetic field.
Force on Moving Charge
A charge experiences a force if it travels across a magnetic field. The force on a moving charge in a magnetic field is given by the formula,
F = q.v.B.sin θ
where,
- q is the Charge
- B is the Magnetic Field
- v is the Velocity of the Charge
- θ is the Angle Between Magnetic Field and Velocity of Charge
Magnetic Effect Of Current
Moving charge produces electric field and this shown in the experiment added below:
In the above material if the current pass through the copper wire then it deflects the compass placed near it. This shows that moving charges produces electric filed.
Right-Hand Rule
The right-hand Rule is used to determine the direction of the force (F) in a magnetic field. Right-Hand Rule states that,
Point your pointer finger towards the direction of the charge’s motion. Between v and B, rotate your middle finger away from your index finger. Hold your thumb parallel to the plane produced by your index and middle fingers. If the charge q is positive, your thumb will point in the direction of the force (F). The image added below shows the Right Hand Rule.
Uses of Magnets
Various uses of the magnets are,
- Magnets is used in magnetic compass to gets the direction.
- Magnets are used in Speakers and others.
- Magnets are used in Electric Motors and Electric Dynamos.
- Electromagnets are used in Maglev Trains and others.
- Magnets are used in construction industries.
One of the most important use of Magnetism is, Magnetism Separation of various objects.
Magnetism Separation Method
Magnetism Separation is the process of separating various metallic impurities and other thing form the ore, or separating metallic ore from the non-metallic impurities. Eg. Iron metal is separated from magnetite by magnetism separation method.
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Example on Magnetic Force Formula
Example 1: Find magnetic force on a charged particle travelling at 5 m/s in a magnetic field of 2 T? Its field’s direction is the same as the route of the charged particle. (Given q = 40 C)
Solution:
Given:
- Charge, q = 40 C
- Velocity, v = 5 m ⁄ s
- Magnetic Field, B = 2 T
Because the second particle’s route difference is the same as the direction of its field, θ = 30°
F= q v B sin θ
F = 40 × 5 × 2 × sin 0°
F = 0
Hence, the magnetic force of charged particles is 0 N.
Example 2: Find the particle force on a charged particles travelling at (v) 20 m/s in a magnetic field of (B) 10 T? If the angle between q and B is 30° (Given q = 4 C)
Solution:
Given:
- Charge, q = 4 C
- Velocity, v = 20 m ⁄ s
- Magnetic Field, B = 10T
- θ = 30°
F= q v B sin θ
F = 4 × 20 × 10 × sin 30°
F = 400 N
Hence, the magnetic force of charged particles is 400 N.
Magnetism – FAQs
What is Magnetism?
Magnetism is the property of the object that is responsible for the magnetic behaviour of the material.
What is Magnetic Force?
The magnetic force between two moving charges can be defined as the impact of one charge’s magnetic field on the other.
What is Importance of Magnetic Field Lines?
Magnetic Field Lines are important because,
- They indicate the Direction of Magnetic Field.
- Intensity of a magnetic field is proportional to the number of magnetic field lines present in a given region, etc.
Do Earths have a Magnetic Field?
Yes, Earth also have a magnetic field due its moving iron core . Earth’s Magnetic Field is responsible for the gravity of the Earth.
What is Magnetism for Class 6?
Magnetism is the property of the property of the material that is responsible for the magnetic behaviour of the material.
What is Magnetism Formula?
The magnetic formula for the material is,
F = B.I.L sin θ
where,
- B is the Magnetic Field Strength
- I is the Current in the Material
- L is the Length of the Material
What is the Law of Magnetism?
Law of Magnetism states that,
“Like Poles repel each other and Unlike Poles attracts each other.”
What is Magnetic Energy?
Magnetic Energy is the energy associated with the magnetic field and is responsible for magnetic work done.
What is Permanent Magnetism?
If a magnet regain its magnetism after the removal of the magnetizing force then it is called the Permanent Magnetism.
What is Temporary Magnetism?
If a magnet looses its magnetism after the removal of the magnetizing force then it is called the Temporary Magnetism.
Who discovered Magnetism?
A physicist from United Kingdom named William Gilbert is credited for the discovery of magnetism.
What is Magnetism Energy?
Magnetism is a type of force but not energy. Energy due to Magnet is called Magnetic Energy.
Bar Magnet
Bar Magnet is a magnet that is rectangular in shape and has two poles, the North Pole and South Pole. The magnetic field of a bar magnet is maximum at its pole and minimum at its center. Bar Magnets are made up of Iron, cobalt, or any other Ferromagnetic materials that show magnetic properties. Bar magnets can be of various types including Cylindrical Bar magnets and Rectangular Bar magnets.
Bar magnets have fascinated us for centuries due to their practical applications in everyday tools and advanced technologies. In this article, we will dig deep into What a is Bar Magnet, the Properties of the Bar Magnet, the Application of Bar Magnet, and others in detail.
Table of Content
What is Bar Magnet?
A bar magnet is a rectangular piece typically made from iron, steel, or a ferromagnetic substance, having distinct north and south poles. Even if it’s broken, each fragment will maintain its unique identity with retained poles.
Bar Magnet Diagram
The basic diagram of the Bar Magnet is added in the image below,
Bar Magnet
Poles of Bar Magnet
A bar magnet has two poles:
- North Pole
- South Pole
These poles play an important role in magnet’s behavior and interactions.
Types of Bar Magnet
Various types of the bar magnets are added in the article below,
- Alnico Bar Magnet
- Neodymium Bar Magnet
- Cylindrical Bar Magnet
- Rectangular Bar Magnet
Alnico Bar Magnet
Alnico bar magnets offer excellent temperature stability, high residual induction, and relatively high energies. They have better corrosion resistance and usually do not require surface treatment. It has temperature stability, with a working temperature of 300-500°C, and they demagnetize at temperatures exceeding 600°C. Due to their strategic resources of cobalt and nickel, alnico magnets are relatively expensive and find applications in aerospace, military, automotive industry, and security systems.
Neodymium Bar Magnet
Neodymium bar magnets are widely used in electronics, electrical machinery, medical equipment, toys, packaging, hardware machinery, aerospace, and other fields. They are known for their exceptional magnetic strength and versatility, making them popular in various industries and scientific applications. Neodymium bar magnets come in a range of grades, offering exceptional magnetic strength and adaptability. However, they are sensitive to temperature and can be significantly affected by exposure to elevated temperatures.
Cylindrical Bar Magnet
A bar magnet of the shape of a cylinder is called a cylindrical bar magnet. It is also called Rod Magnet.
Rectangular Bar Magnet
Normal bar magnet that is in shape of a cuboid is called a Rectangular bar magnet. It has various applications and in general is called Bar mangnets.
Properties of Bar Magnet
Various properties of a Bar Magnet are,
- Directional Property: When suspended freely a Bar Magnet always comes to rest in the geographically north-south direction.
- Magnetic Induction: When a magnetic material is kept in contact with a bar magnet, it acquires magnetic properties through magnetic induction.
- Demagnetization: A bar magnet loses its magnetism when heated, beaten hard by a hammer, or kept under AC current.
- Attractive Property: The bar magnet attracts ferromagnetic materials like iron, cobalt and nickel.
- Existence as a Dipole: Bar magnet always exists as a dipole, and the existence of a monopole is not possible
Magnetic Field of a Bar Magnet
Magnetic field of a bar magnet is created by the motion of electrons in the material that forms the magnet. It’s Magnetic force is strongest at the poles. The magnetic field of a bar magnet is very similar to the electric field created by an electric dipole.
The magnetic field of a Bar Magnet is shown in the image added below,
Magnetic Field Lines Around a Bar Magnet
Magentic field lines are the imaginary lines that are used to represent the strength of a magnet. These lines start from the north pole of the magnet and goes to the south pole of the agent. Properties of the magnetic field are added below,
- For a bar magnet, the magnetic field lines form closed loops, extending from the north pole to the south pole.
When two bar magnets are brought close to each other, their magnetic lines of force interact with each other and get modified to point in the direction of the resultant magnetic force (field).
Pole Strength of Bar Magnet
The pole strength of a bar magnet is the strength of a magnetic pole to attract magnetic materials towards itself. The magnetic force of a bar magnet is strongest at the poles. The pole strength is related to the magnetic moment of the magnet, and it is the product of the pole strength and the length of the magnet.
Formula of Pole Strength
Formula to find pole strength of a bar magnet is given by:
P = W/T
Where,
- P is the Strength of Magnetic Pole
- W is the Work Done in Moving Magnet around the Wire
- I is Electric Current in Wire
SI Unit of Pole Strength
- SI Unit of pole strength of a bar magnet Ampere-meter (A.m).
- Dimension of Pole strength is, [LA]
Applications of Bar Magnets
Bar magnets have various applications in different fields which are as follows:
- Picking up Small Metallic Objects: Bar magnets are used to pick up small metallic objects such as metal shavings, nails, and screws, as well as magnetic stirring rods in laboratory settings.
- Industrial purposes: Bar magnets are used for industrial applications such as collecting magnetic waste or separating magnetic objects from a large area of mixed substances. They are also used for stirring mixtures to facilitate the mobility of ferromagnetic substances in chemical experiments.
- Electronic Devices: Bar magnets find applications in electronic devices such as televisions, microphones, and mobile phones.
Uses of Bar Magnet
Various uses of the bar magntes are,
- Magnetizing Objects: Bar magnets can be used to magnetize other objects such as paperclips, by stroking the object against the bar magnet
- Compass: When freely suspended the bar magnet aligns itself to earth’s magnetic field making it useful as a compass to find north and south direction.
Bar Magnet as Equivalent Solenoid
A bar magnet can be modeled as an equivalent solenoid. The magnetic moment of a bar magnet as an equivalent solenoid can be derived by calculating the axial field of a finite solenoid carrying current. The similarity between magnetic field lines of a bar magnet and solenoid is that a bar magnet can be thought of as a large number of circulating currents in analogy with a solenoid. The image of magnetic field of a Solenoid is added below,
Read more about Magnetic Field of a Solenoid.
Difference between Bar Magnet and Electromagnet
The key difference between a bar magnet and an electromagnet lies in their magnetic properties:
- Electromagnet: An electromagnet, is a temporary magnet that can produce a magnetic field in the presence of electric current. It is formed when electric current is passed through wires wound around a soft metal core. The strength of the magnetic field produced by an electromagnet can be varied by controlling the electric current that passes through the wire. However, an electromagnet loses its magnetism once the current flow is stopped, requiring a continuous power supply to maintain the magnetic field.
- Bar Magnet: A bar magnet is a permanent magnet that can create its own persistent magnetic field. It has a fixed magnetic field strength and does not require an external power source to maintain its magnetism. The magnetism in a bar magnet is caused by the alignment of electron spins within the material, resulting in a constant magnetic field.
Read More,
FAQs on Bar Magnets
1. What is a Bar Magnet?
A bar magnet is a rectangular piece typically crafted from Iron, steel, or a ferromagnetic substance. It has two poles – a north and a south pole.
2. What is Magnetic Field Lines of a Bar Magnet?
Magnetic field lines around a bar magnet form closed loops, and their patterns are visualized using iron filings in the presence of the magnet. These patterns distinctly showcase the intensity and direction of the magnetic field.
3. What is Pole Strength?
Pole strength refers to the strength of the magnetic poles of a magnet. For a bar magnet, it’s the potency of the north and south poles. The force exerted by a bar magnet is most potent at its poles, and the interaction between like poles results in repulsion, while unlike poles attract.
4. What are Uses of Bar Magnets?
Bar magnets have various applications in laboratories, educational settings, and everyday life. Some common uses of bar magnets include picking up small metallic objects, demonstrating magnetic fields, experimenting with magnetic fields, and industrial purposes.
5. What is Magnetic Field of a Bar Magnet?
The magnetic field of a bar magnet is created by the motion of electrons in the material that forms the magnet.
6. How is a Bar Magnet Different from an Electromagnet?
Bar magnet is a permanent magnet that can create its own persistent magnetic field, while an electromagnet is a type of temporary magnet that can produce magnetic field in the presence of an electric current.
7. What Metal is a Bar Magnet?
Bar magnet is made of different metals like Iron, Cobalt and Nickel.
8. What are Three Properties of a Bar Magnet?
- Attractive Property: To attract ferromagnetic materials
- Directional Property: When suspended freely it comes in alignment to north-south direction.
- Existence as a Dipole: Bar magnets always exists as a dipole and existence as a monopole is not possible.
9. What are Poles of a Bar Magnet?
The bar magnet has two poles, a north pole and a south pole. The magnetic force is strongest at these poles.
10. Where are Poles of a Bar Magnet Located?
The poles of a bar magnet are located at its ends. One end is called the north pole, and the other end is called the south pole. These poles are where the magnetic field lines converge (south pole) and diverge (north pole).
11. Is there any Magnetic Field Lines of Force inside a Bar Magnet?
Yes, there are magnetic field lines of force inside a bar magnet. The magnetic field lines emerge from the north pole, traverse through the interior of the magnet, and re-enter at the south pole. The lines form a continuous loop, indicating the magnetic field’s presence within the magnet.
Gauss’s Law
Gauss law is defined as the total flux out of the closed surface is equal to the flux enclosed by the surface divided by the permittivity. The Gauss Law, which analyses electric charge, a surface, and the issue of electric flux, is analyzed. Let us learn more about the law and how it functions so that we may comprehend the equation of the law.
What is Gauss Law?
According to gauss law, the total electric flux out of a closed surface is equal to the charge contained divided by the permittivity. The electric flux in a given area is calculated by multiplying the electric field by the area of the surface projected in a plane perpendicular to the field. The total flux associated with a closed surface equals 1 ⁄ ε0 times the charge encompassed by the closed surface, according to the Gauss law.
∮ E.ds = q ⁄ εo
For example, a point charge ‘q’ is put within a cube with the edge ‘a’. The flux across each face of the cube is now q ⁄ 6εo, according to Gauss law. The electric field is the most fundamental concept in understanding electricity. In general, the electric field of a surface is computed using Coulomb’s law; however, understanding the idea of Gauss’ law is required to calculate the electric field distribution in a closed surface. It describes how an electric charge is enclosed in a closed surface or how an electric charge is present in a closed surface that is enclosed.
Gauss Law Formula
According to the Gauss law formula, the total electric charge enclosed in a closed surface is proportional to the total flux enclosed by the surface. As a consequence, the total electric charge Q contained by the surface is: if ε0 is electric constant and ϕ is total flux.
Q = ϕ εo
The formula of Gauss law is given by:
ϕ = Q⁄εo
Where,
- εo is electrostatic constant,
- Q is total charge within a given surface, and
- ϕ is flux enclosed by surface.
The Gauss Theorem
The Gauss theorem connects the ‘flow’ of electric field lines (flux) to the charges within the enclosed surface in simple terms. The net charge in the volume contained by a closed surface is exactly proportional to the net flux through the closed surface.
ϕ = E.dA = qnet ⁄ εo
The net electric flow stays 0 if no charges are contained by a surface. The number of electric field lines entering the surface equals the number of field lines exiting the surface.
A corollary of the gauss theorem statement:
The electric flux from any closed surface is only due to the sources and sinks of electric fields enclosed by the surface. The electric flux is unaffected by any charges outside the surface. Furthermore, only electric charges may operate as electric field sources or sinks. It is important to note that changing magnetic field cannot act as electric field sources or sinks.
As it encloses a net charge, the net flow for the surface on the left is non-zero. Because the right-hand surface does not contain any charge, the net flow is zero. The Gauss law is nothing more than a repetition of Coulomb’s law. Coulomb’s law is readily obtained by applying the Gauss theorem to a point charge surrounded by a sphere.
Note: Gauss’ law and Coulomb’s law are closely related. If gauss law is applied to a point charge in a sphere, it will be the same as applying coulomb’s law.
Gauss Law Equation
Gauss law equation can be understood using an integral equation. Gauss’s law in integral form is mentioned below:
∫E.dA = Q/ε0 ⇢ (1)
Where,
- E is the electric field
- Q is the electric charge enclosed
- ε0 is the electric permittivity of free space
- A is the outward pointing normal area vector
Flux is a measure of the strength of a field passing through a surface. Electric flux is given as:
Φ = ∫E⋅dA ⇢ (2)
Application of Gauss Law
There are different formulae obtained from the application of Gauss law for different conditions. Below are some well-known applications of Gauss law:
- In a medium with a dielectric constant of K, the strength of the electric field near a plane-charged conductor E = σ ⁄ K εo. Eair = σ ⁄ εo when the dielectric medium is air.
- At a distance of ‘r’ in the case of an infinite charge line, E = (1 ⁄ 4 × π r ε0) (2π ⁄ r) = λ ⁄ 2π r εo, where λ is linear charge density.
- In a condenser or capacitor, the field between two parallel plates is E = σ ⁄ ε0, where σ is the surface charge density.
- The electric field strength near a plane sheet of charge is E = σ ⁄ 2K εo, where σ is the surface charge density.
- For a charged ring having a radius ‘R’, from the centre of the ring at a distance ‘x’, here, the electric field becomes:
Gauss Law Derivation – Electric Field due to Infinite Wire
To find the electric field due to an infinite wire, assume the charge per unit on the infinitely long wire is λ. The electric field is radially away from all points of the wire, and no component is parallel to the line of charge. Now, assume the wire as a cylinder (with radius ‘r’ and length ‘l’) centered on the line of charge as the gaussian surface.
The electric field is perpendicular to the cylinder. Hence, the angle between the electric field and area vector is 0°. So, cosθ = 1. The top and bottom of the cylinder are parallel to the electric field. Hence, the area vector here is 90° w.r.t. the electric field. Therefore, cosθ = 0. Hence, we can say that the electric flux occurs only due to the curved surface of the cylinder. According to gauss law:
ϕ = E.d ⇢ A
ϕnet = ϕcurved + ϕtop + ϕbottom
ϕ = E.d ⇢ A = ∫E.dA cos0 + ∫E.dA cos90 + ∫E.dA cos90
ϕ = ∫E.dA
The curved surface is equidistant from the line of charge due to its radial symmetry. So, the electric field on the surface has a constant value throughout the surface.
ϕ = ∫E.dA = ∫E. 2πrl
The net charge enclosed by the surface:
qnet = λ.l
Now, using gauss theorem:
ϕ = ∫E. 2πrl = qnet ⁄ εo = λ.l/εo
∫E. 2πrl = λ.l/εo
E = λ/2πrεo
Solved Examples on Gauss Law
Example 1: In the x-direction, there is a homogeneous electric field of size E = 50 N⁄C. Calculate the flux of this field across a plane square area with an edge of 5 cm in the y-z plane using the Gauss theorem. Assume that the normal is positive along the positive x-axis.
Solution:
Given:
Electric field, E = 50 N⁄C
Edge length of square, a = 5 cm = 0.05 m
The flux of the field across a plane square, ϕ = ∫ E cosθ ds
As the normal to the area points along the electric field, θ = 0.
Also, E is uniform so, Φ = E ΔS = (50 N⁄C) (0.05 m)2 = 0.125 N m2 C-1.
Hence, the flux of the given field is 0.125 N m2 C-1.
Example 2: There are three charges, q1, q2, and q3, having charges 4 C, 7 C, and 2 C enclosed in a surface. Find the total flux enclosed by the surface.
Solution:
Total charge Q,
Q = q1 + q2 + q3
= 4 C + 7 C + 2 C
= 13 C
The total flux, ϕ = Q ⁄ ε0
ϕ = 13 C ⁄ (8.854×10−12 F ⁄ m)
ϕ = 1.468 N m2 C-1
Therefore, the total flux enclosed by the surface is 1.584 N m2 C-1.
Example 3: Two conducting plates having charges Q1 and Q2, are kept parallel to each other. Find the distribution on all four surfaces.
Solution:
It can be seen from the figure that two faces lie inside the conductor when E = 0. The flux is also 0. The faces that are outside are parallel to the electric field, the flux there will be 0 too. Therefore, the total flux of the electric field is 0.
From gauss law, the total charge inside the closed surface must be 0. Therefore, the charge on the inner side of one plate should be equal to the charge on the other side.
Using the equation E = σ/2ε0, the electric field at P:
- Due to the charge Q1 – q = (Q1 – q)/2Aε0 (downward).
- Due to the charge +q = +q/ε0 (upward).
- Due to the charge Q2 + q = (Q2 + q)/2Aε0 (upward)
- Due to the charge -q = -q/ε0 (downward).
The net electric field is in the downward direction:
(Q1 – q)/2Aε0 + (-q/ε0) + (Q2 + q)/2Aε0 + +q/ε0
Q1 -q +q -Q2 = 0
q = (Q1 – Q2)/2
Q1 – q = (Q1 + Q2)/2
Q2 + q = (Q1 + Q2)/2
Example 4: What is the differential form of the Gauss theorem?
Solution:
The electric field is related to the charge distribution at a certain location in space by the differential version of Gauss law. To clarify, according to the law, the electric field’s divergence (E) is equal to the volume charge density (ρ) at a given position. It’s written like this:
ΔE = ρ ⁄ ε0
Here, ε0 is the permittivity of free space.
Example 5: There are three concentric spherical shells A, B, and C with radii a, b, and c. The charges are present on shells A and C (q and -q respectively), and shell B is earthed. Find the total charges appearing on B and C.
Solution:
Since the inner surface of shell B must have a charge of -q, suppose the outer surface of B has a charge ‘x’. Then, the inner surface of C must have a charge of ‘-x’.
Potential due to charge ‘q’ on A = q/4πε0b
Potential due to ‘-q’ on inner surface of B = -q/4πε0b
Potential due to ‘x’ on outer surface of B = x/4πε0b
Potential due to ‘-x’ on inner surface of C = -x/4πε0c
Potential due to ‘x – q’ on inner surface of C = x – q/4πε0c
Now, the net potential: VB = x/4πε0b – q/4πε0c
This potential is equated to 0 as the shell B is earthed.
Therefore, x = qb/c
Below is the figure showing the charges on each surface:
FAQs on Gauss Law
Question 1: State Gauss law.
Answer:
Gauss law states that the net flux of an electric field is directly proportional to the charge enclosed in a closed surface.
Question 2: How do we choose an appropriate Gaussian Surface for different cases?
Solution:
In order to select an acceptable Gaussian Surface, we must consider the fact that the charge-to-dielectric constant ratio is supplied by a (two-dimensional) surface integral over the charge distribution’s electric field symmetry.
We’ll need to know about three potential scenarios.
- When the charge distribution is spherically symmetric, it is called spherical.
- When the charge distribution is cylindrically symmetric, it is called cylindrical.
- When the charge distribution exhibits translational symmetry along a plane, it is called a pillbox.
Depending on where we want to compute the field, we may determine the size of the surface. The Gauss theorem is useful for determining the direction of a field when there is symmetry, as it informs us how the field is directed.
Question 3: State gauss law in electrostatics.
Solution:
Gauss law in electrostatics states that the electric flux through any closed surface is equal to the net charge enclosed by the surface divided by the permittivity of free space.Normally, the Gauss law is employed to calculate the electric field of symmetric charge distributions. When using this law to solve the problem of the electric field, there are numerous processes required. The following are the details:
- First, we must determine the charge distribution’s spatial symmetry.
- The next step is to select a proper Gaussian surface that has the same symmetry as the charge distribution. Its ramifications must also be determined.
- Calculate the flux across the surface by evaluating the integral ϕs E over the Gaussian surface.
- Calculate the amount of charge contained within the Gaussian surface.
- Calculate the charge distribution’s electric field.
However, in order to determine the electric field, pupils must remember the three forms of symmetry. The following are the several forms of symmetry:
- Symmetry on a sphere
- Symmetry in a cylindrical shape
- Symmetry on a plane
Question 4: What are the applications of Gauss law?
Answer:
Complex electrostatic problems involving symmetry like cylindrical, spherical, etc. can be solved using Gauss law. It also helps solving for the electric field that involves complex calculations.
Question 5: What is Gaussian surface?
Answer:
Gaussian surface is the surface through which electric flux is calculated.
Question 6: State Gauss law for magnetism.
Answer:
Gauss law for magnetism states that the magnetic flux across any closed surface is 0. This can be written as Div. B = 0, where Div. B is the divergence factor of B.
Gauss’s Law is a fundamental principle in physics that relates the electric field to the distribution of electric charges. It states that the total electric flux through any closed surface is equal to the total charge enclosed by the surface divided by the permittivity of free space (ε0). Mathematically, Gauss’s Law can be expressed as:
∮S E · dA = Qenc/ε0
where ∮S represents the surface integral over a closed surface S, E is the electric field vector, dA is the surface area vector, Qenc is the total charge enclosed by the surface, and ε0 is the permittivity of free space.
Gauss’s Law is a powerful tool for calculating electric fields in situations where the symmetry of the charge distribution makes it difficult to use Coulomb’s Law. By using Gauss’s Law, it is possible to calculate the electric field of a uniformly charged sphere, cylinder, or plane, for example.
Gauss’s Law has important applications in many areas of physics, including electromagnetism, electrostatics, and quantum mechanics. It is used to analyze the behavior of electric fields in charged particles, capacitors, and other electrical devices. It also plays a key role in the understanding of electromagnetic radiation and the propagation of radio waves.
Magnetization and Magnetic Intensity
We’ve all had fun with magnets as kids. Some of us are now even playing with them! What makes them magnetic though? Why aren’t there magnetic fields in all materials and substances? Have you ever given it any thought? The subjects of magnetization and magnetic intensity will be covered in this chapter.
Magnetization
Magnetization is caused by a magnetic moment, as we all know. This is caused by the mobility of electrons in atoms. The response of a substance to an external magnetic field determines its net magnetization.
It also takes into account any imbalanced magnetic dipole moment that the material may have due to the mobility of its electrons, as previously indicated. The idea of magnetization aids in the classification of materials according to their magnetic properties.
We’ll learn more about magnetization and the idea of magnetic intensity in this part. The arrangement of the atoms inside a material determines a magnet’s magnetic behaviour. This is what we’ll be discussing in this article. The magnetization (M) of the material is equal to the net magnetic moment per unit volume of that material.
In terms of mathematics,
M = mnet ⁄ V
Let’s take a look at the case of a solenoid. If we consider a solenoid with n turns per unit length and a current I flowing through it, the magnetic field in the solenoid’s interior may be expressed as,
B0 = μ0 n I
where, µ0 is the constant permeability of a vacuum.
If we fill the solenoid’s inside with a non-zero magnetization material, the field within the solenoid must be higher than before. Inside the solenoid, the net magnetic field B may be written as,
B = B0 + Bm
where, Bm is the field provided by the core material.
It is proportional to the material’s magnetization in this case. In terms of mathematics,
Bm = μ0 M
Let us now look at another concept: a material’s magnetic intensity. A material’s magnetic intensity can be expressed as,
H = (B ⁄ μ0) − M
The total magnetic field may alternatively be defined as, as shown by this equation.
B = μ0 (H + M)
H denotes the magnetic field owing to external variables such as the current in the solenoid, whereas M denotes the magnetic field due to the nature of the core. The latter amount, M, is influenced by external factors and is given by.
M = χ H
where, χ is the material’s magnetic susceptibility.
Magnetic susceptibility is a measurement of a material’s reaction to an external field. For paramagnetic materials, the magnetic susceptibility is small and positive, while for diamagnetic materials, it is tiny and negative.
Substitute the value of M in the equation of B.
B = μ0 (H + χ H) = μ0 (1 + χ) H
= μ0 μr H = μ H
Here, μr is the relative magnetic permeability of the material which is comparable to the dielectric constants in electrostatics. The magnetic permeability is defined as follows:
μ = μ0 μr = μ0 (1 + χ)
Magnetic Intensity
The arrangement of the atoms inside a material determines a magnet’s magnetic behaviour. When a ferromagnetic substance is subjected to a strong external magnetic field, it experiences a torque, which causes the substance to align itself in the direction of the applied magnetic field and therefore become strongly magnetised in that direction.
The force that a unit north – pole experiences when it is put in a magnetic field is described as the magnetic intensity at that location. The magnetic field strength at P owing to a single pole is given by:
The magnetic field B, we argue, may be expressed as:
B = (μ0 ⁄ 4 π) (m / π r2)
We know, μ0 ⁄ 4 π = 10−7
⇒ B = 10−7 × (m / π r2)
where, m is the pole strength.
The Intensity of Magnetic Field due to a Magnet at Different Points
- In Longitudinal Position
The +⁄-m is the magnitude of the south and north poles, respectively. r is the distance between point P and the magnet’s centre. The length of the bar magnet is denoted by the letter l. The magnetic field intensity at point P is given by:
B = (μ0 ⁄ 4π) (2M r ⁄ r2 − l2)
where, M is the magnetic moment and (2ml) is the length of the magnetic moment.
For a small magnet, r2 >> l2:
B = (μ0 ⁄ 4π) (2M ⁄ r3)
- In Transverse Position
The magnetic field intensity at point P is given by,
B = (μ0 ⁄ 4π) (M ⁄(r2 + l2)3 ⁄ 2)
For a small magnet, r2 >> l2:
B = (μ0 ⁄ 4π) (M ⁄ r3)
⇒ B ∝ 1 ⁄ r3
Definition of Intensity of Magnetisation
When a magnet is put in a magnetic field, it changes its magnetic moment. The Intensity of Magnetisation is defined as the change in the magnetic moment per unit volume.
The formula of Intensity of Magnetisation is given as:
I = M ⁄ V
Magnetic moment, M = m x
Volume, V= A x
⇒ I = m x ⁄ A x = m ⁄ A
where,
- m is the pole strength,
- A is the area of cross-section,
- x is the length of the magnet, &
- I is the intensity of magnetisation.
Sample Questions
Question 1: What is the distinction between Magnetic Intensity and Magnetisation Intensity?
Answer:
The magnetic intensity of a magnet specifies the forces experienced by its poles in a magnetic field, whereas the intensity of magnetization explains the change in a magnet’s magnetic moment per unit volume.
Question 2: What exactly do you mean when you say “induced magnetization”?
Answer:
Induced magnetization is a method of making a non-magnetic substance magnetic. When you put it under the influence of an external magnetic field, you may do so.
Question 3: What is the formula for magnetic intensity, and what does it mean?
Answer:
The magnetic field strength at a particular place can be expressed as a vector quantity known as the magnetic intensity, abbreviated as H. Letter H, on the other hand, equals nI. The magnetic intensity unit is given as A ⁄ m, and its dimensions are [L−1M0T0I1].
Question 4: What is the definition of magnetic intensity?
Answer:
The magnetic moment per unit volume of the magnetised material is stated to be defined as the intensity of magnetism, thus we may write it down as I = M ⁄ V, where M is the total magnetic moment inside volume owing to the magnetising field.
Question 5: What is induced magnetisation, and how does it work?
Answer:
The process of causing a non-magnetic substance to become magnetised by exposing it to an external magnetic field is known as induced magnetisation.
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