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Electromagnetic Induction refers to a process in which a conductor is put in a specific position and the magnetic field is varying or the magnetic field is stationary and the conductor moves. This produces Electromotive Force (EMF) across the electrical conductor. Electromagnetic induction is a non-contact phenomenon in which the inter-relation between electric field and magnetic field was depicted. It is used to produce electricity, especially from the rotation of a magnet around a stationary conductor without using batteries. Motors, generators, and transformers work on the electromagnetic induction principle.
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Key Terms: Electromagnetic Induction, Magnetic Flux, Conductor, Magnetic Field, Electric Field, Batteries, Transformers
What is Electromagnetic induction?
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Electromagnetic Induction is a current produced by the voltage production due to a changing magnetic field. This happens in one of the two conditions:-
- When we place the conductor in a changing magnetic field. (when using an AC power source)
- When the conductor constantly moves in a stationary field.
Electromagnetic Induction was discovered in 1831 by Michael Faraday. Michael Faraday conducted an experiment where he connected the wires to a voltmeter (a device used to measure voltage) and wrapped them around a bar magnet. He then moved the magnet and noticed the changes in the voltage. After conducting the experiments, he concluded that the factors that affect the voltage are-
- The number of coils – The induced voltage is directly proportional to the number of turns in the wire. The greater the number of turns, the more the voltage is produced.
- Change in the Magnetic Field – Any change in the magnetic field affects the production of voltage. Magnetic field experiences change either by moving the magnet around the conductor or vice versa.
Faraday’s Law of Electromagnetic Induction Detailed Explanation
Faraday’s Laws of Electromagnetic Induction Video Explanation
Read Also:
| Related Topics | ||
|---|---|---|
| Energy Consideration | Inductance | Electromagnetism |
| Unit of Inductance | Faraday Constant | Unit of Magnetic Flux |
| Motional emf | Types of generators | Uses of Inductor |
Electromagnetic Induction Formula
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The electromagnetic induction is mathematically represented as:-
e = N × dΦ/dt
Where
- e = induced voltage
- N = number of turns in the coil
- Φ = Magnetic flux (amount of magnetic field present on the surface)
- t = time
Magnetic Flux
Similar to electric flux, the magnetic flux in a surface is the measure of the magnetic field on a surface. In a closed surface, it is mathematically defined as the surface integral of the magnetic field through the surface.
Φ B = B.A = BA cosθ
Where, θ represents the inclination between B and A
Principle of Electromagnetic Induction
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Electromagnetic Induction works on the principle that the EMF induced in a loop by a changing magnetic flux is equal to the rate of change of the magnetic flux through the loop.
- Transformers, electric generators, motors, and wireless communication devices work on this principle of electromagnetic induction.
- Faraday's Law states that EMF will be induced by a change in the magnetic environment of a coiled wire.
Applications of Electromagnetic Induction
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Some of the applications of electromagnetic induction are:-
- Data storage is done by recording through magnetic fields. In some computers, hard drive data is recorded on a coated spinning disk.
- Tablets used by graphic designers also work on electromagnetic induction. A battery-operated pen is used on a screen connected by several wires. The magnetism from the tip induces EMF on the screen, translating into graphical images.
- Electric vehicles also work on electromagnetic induction.
- It is also used to treat patients with mental disorders such as depression and hallucinations by transcranial magnetic stimulation (TMS). Here, magnetic stimulation is applied to specific areas of the brain to bring relief.
- The working of an AC generator is dependent on this concept.
- Transformers use the concept of induction.
- The magnetic flow meter works on electromagnetic induction.
Electromagnetic induction in AC generator
As the coil of an AC generator rotates in a magnetic field B, the effective area of the loop is A cosθ, where θ denotes the angle between A and B.
- This produces a flux change which is the principle of operation of an AC generator.
- The axis of the rotation coil is perpendicular to the magnetic field direction.
- The rotation causes the magnetic flux through it to change, hence an EMF is induced in the coil.
Electrical Transformers
An important application of the electromagnetic induction principle is an electrical transformer.
- A transformer is a device changing AC electric power from one voltage level to another level through a magnetic field.
- A step-down transformer is one in which voltage is higher in primary than the secondary voltage.
- However, the one in which the secondary voltage has more turns comparatively is known as a step-up transformer.
- Power companies use a step-up transformer to boost voltage to 100 kV reducing the current and minimizing the loss of power in transmission lines.
- Household circuits use step-down transformers to decrease voltage to 120 or 240 V.
Faraday’s Laws of Induction
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Faraday’s Law of induction states that the magnitude of the induced voltage (emf) in a circuit is equal to the rate of change of magnetic flux through it. The relationship can be depicted as –
ε = -N(dΦ/dt)
- Where Φ is the magnetic flux
- t is the time
- and N is the number of turns in the coil.
The negative sign in the formula is due to Lenz's law, as explained below.
Lenz’s law
This law states that the direction of the induced current is such that it opposes the cause which produces it, i.e., the change in magnetic flux. Lenz's law is based on the principle of energy conservation.
Emf = – NΔΦ/ Δt
Eddy currents
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By Lenz's law of electromagnetic induction, current swirls to create a magnetic field that opposes a change. Therefore, eddy currents lead to a loss of energy.
- Brakes of trains: During braking, brakes expose the metal wheels of the train to a magnetic field that produces eddy currents. This magnetic interaction slows down the wheels. The faster the wheels spin, the stronger the effect. Hence, as the train slows, the braking force is reduced, which produces a smooth stopping motion.
- Galvanometers: Some galvanometers have a fixed core of nonmagnetic metallic material. When the coil oscillates, eddy currents in the core oppose the motion to bring it to rest.
- Induction furnace: The eddy currents produced in the metals produce a high temperature to melt them.
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Important Topics for JEE MainAs per JEE Main;2024 Session 1, important topics in the Chapter Electromagnetic Induction are as follows:
Some of the important questions from JEE Main 2024 Session 1 are given below: 1. A rectangular loop of length 2.5 m and width 2 m is placed at \(60°\)to a magnetic field of 4 T . The loop is removed from the field in 10 sec.The average emf induced in the loop during this time is ? 2. A small square loop of wire of side l is placed inside a large square loop of wire of side L(L=l2). The loops are coplanar and their centers coinside. The value of the mutual inductance of the system is \(\sqrt x \times 10^{-7}\) H, where x = _____ |
Things to Remember
- Electromagnetic induction is the production of current and EMF in a circuit as a result of the change in the magnetic field.
- EMF produced in a circuit depends on the number of turns in the coil and changes in the magnetic field.
- The electromagnetic induction formula is given as e = N × dΦ/dt.
- AC generators and Electrical Transformers are some of the important applications of electromagnetic induction.
- Faraday’s Law of induction states that the magnitude of EMF in a circuit is equal to the rate of change of magnetic flux through it.
Previous Year Questions
- If a transformer of an audio amplifier has output impedance 8000 0 and the speaker has input impedance…...[JCECE 2005]
- A conducting loop in the shape of a right angled isosceles triangle of height 10cm10cm is kept such that the 90∘ vertex is…..[JEE Advance 2016]
- A 10m long horizontal wire extends from North East to South West. It is falling with a speed of 5.0ms−1……. [ JEE Main 2019]
- If a current of 2.0A2.0A flows through the smaller loop, then the flux linked with bigger loop is…… [JEE Main 2013]
- A coil of cross-sectional area A having n turns is placed in a uniform magnetic field B….. [JEE Main 21018]
- A copper rod of mass m slides under gravity on two smooth parallel rails, with separation ll and set at an angle of θ with the horizontal….. [JEE Main 2018]
- A copper wire is wound on a wooden frame, whose shape is that of an equilateral…. [JEE Main 2019]
- A metallic rod of length ll is tied to a string of length 2l and made to rotate with angular speed…. [JEE Main 2013]
- A square frame of side 10 cm and a long straight wire carrying current 1 A are in the plane of the paper…. [JEE Main 2014]
- If the rod makes n rotations per second, then the time averaged magnetic moment of the rod is… [JEE Main 2019]
- Figure shows a circular area of radius R where a uniform magnetic field….
- In a coil of resistance 100Ω , a current is induced by changing the magnetic flux through it….. [JEE Main 2017]
- When current in a coil changes from 5A to 2A…. [JEE Main 2015]
Sample Questions
Ques 1: When a magnet is accelerated inside the coil, what happens to the current inside it? (1 mark)
Ans. Due to the change in the magnetic field, an emf is induced and as soon as emf is induced, it produces current. Due to the current produced, when the magnet moves inside the coil, the current increases.
Ques 2: The electric current is flowing in a wire in the direction from B to A. Figure out the direction of the current induced in the metallic loop shown below [All India 2014]
Ans. The current that is produced in the wire causes a magnetic field in a vertically downward direction of the coil. According to Lenz’s law, when the direction of current in the wire is from B to A, the current induced in the coil will be in a clockwise direction.
Ques 3: There are two spherical bobs - one composed of metallic, the other of glass. Both of the blobs are of the same size. Which one of the two would reach earlier if they fall free from the same height? State the reason. [Delhi 2014]
Ans. In between the two spherical bobs, the glass bob will reach the ground earlier because glass is an insulator (non-conductor in nature), it only experiences gravitational force whereas since the other bob is metallic in nature, it is induced with eddy current when it falls through the earth’s magnetic field and according to Lenz law, it is induced in the direction opposite to that of the motion of the metallic bob so there’s a delay.
Ques 4: In the given figure, there is a bar magnet that moves rapidly towards a conducting loop that has a capacitor. Determine the polarity of the A and B plates present in the capacitor. [All India 2014, HOTS]
Ans. When the magnet moves towards the coil, flux associated with the coil increases, and according to Lenz’s law, it will oppose the change.
In this diagram, the North Pole is moving towards the magnet therefore the induced current (from the left side) will flow in a way that it behaves like the North Pole. Since the flow of induced current is in the clockwise direction therefore A is supposed to have positive polarity and B is supposed to have negative polarity.
Ques 5: State Faraday’s Law of Electromagnetic Induction.
Ans. Faraday’s law of electromagnetic induction states that a current is induced inside the conductor which is kept in a changing magnetic field. Any movement or changes in the magnetic field of the coil will ultimately result in an induced emf. There are certain ways in which the magnetic field can be changed, they are-
- When the bar magnet is in motion towards or away from the coil.
- When the coil operates in or out of the magnetic field.
- Change in the area where the coil is placed.
- Rotating the coil.
Ques 6: Two identical loops, one of aluminum and the other of copper are rotated with a similar angular speed in the same magnetic field. Compare
The induced emf
The current is produced in two coils. Justify your answer. [All India 2010]
Ans.
- Since induced emf is dependent on the magnetic field and angular frequency of motion and because these two quantities are the same for both the loops that is copper and aluminum loop, induced emf remains the same.
- Since copper is more resistant to the induced current than aluminum, therefore, copper will have more induced current.
Ques 7: Explain in detail, the law that talks about the polarity of the induced emf. [All India 2009]
Ans. Lenz’s law renders the polarity of induced emf. This law states that the polarity of induced emf is such that it tends to produce a current which is supposed to oppose the change in the quantity of magnetic flux that is produced.
Ques 8. A rod of length l is moving in the horizontal direction with a uniform velocity v in the perpendicular direction to its length in a region where a uniform magnetic field is acting in the downward direction. Find the expression for the emf induced which is flowing through the rod
How do you understand this motional emf by taking into effect the Lorentz force acting on the free charge carriers of the conductor? Explain. [All India 2014]
Ans. d∅dt=Bvldt
d∅dt=Bvl=e
According to Lenz law, Fnet = Fe + Fm
At the position of equilibrium, Fnet = 0
Fe + Fm = 0
qE +q(vector v × vector B) = 0
E = - (vector v × vector B)
E = Bvsinθ
E = Bv
So Bvl = φ
Right-hand rule, the direction of flow of current is along an anti-clockwise direction.
Ques 9. The electric current flowing in a wire in the direction from B to A Find out the direction of the induced current in the metallic loop kept the wire as shown in the figure. (2 marks)
Ans. According to Lenz’s law, the direction of induced current will oppose the cause of its production. Hence, the induced current will be in a manner that it will support the current of the wire. (same direction). The direction of the current will be clockwise.
Ques 10. Magnetic flux (Φ) versus current (I) has been plotted in the figure for two inductors A and B. Which has a higher value of inductance (L)? (Delhi 2010)
Ans. Φ = L(di/dt)
Hence, the slope of the graph gives us an idea of the inductance. In this case, ‘A’ has a higher value of inductance.
Ques 11. Give a definition of self-inductance, along with its SI unit (All India 2010)
Ans. Φ = L(di/dt)
Self-inductance is defined as the magnetic flux induced when there is a unit change of current in a unit of time. Its SI unit is Henry (H)
Ques 12. Predict the directions of induced current in both rings 1 and 2 when the current I decreases steadily. (2 marks)
Ans. In the case of the first ring, the induced current is in an Anticlockwise direction.
In the case of the second ring, the current induced is in the clockwise direction.
Ques 13. What will be the direction of the induced current in the rectangular loop abcd when it is moved inside a region of a uniform magnetic field B which is in a direction perpendicular to the direction of the loop abcd? (Comptt. All India 2012)
Ans. The current induced will be in the anti-clockwise direction, i.e. cbadc
Ques 14. Describe the change in mutual inductance of a pair of coils with:
(i) Increase in distance between the coils
(ii)Increase in number of turns in the coils (All India 2013)
Ans. (i)There is a decrease in Mutual inductance because the flux which is linked with the secondary coil decreases.
(ii)An increase in n1 and n2 increases mutual inductance (M)
Ques 15. The motion of a copper plate is damped when it is allowed to oscillate between the two poles of a magnet. What causes this damping? (All India 2013)
Ans. This damping of motion is caused by the eddy current induced in the copper plate.
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