Electromagnetic induction is a pivotal topic in JEE Physics that connects electricity and magnetism. It explains how changing magnetic fields produce electric currents, which is foundational for many electrical devices. This guide covers Faraday's laws, Lenz's law, self and mutual induction, eddy currents, energy in magnetic fields, and real-world applications, supported by essential formulas and examples.
Electromagnetic induction refers to the phenomenon where an electromotive force (emf) is generated in a conductor due to a changing magnetic flux through it. This principle is fundamental in transformers, electric generators, inductors, and many other devices.
The discovery of electromagnetic induction by Michael Faraday in 1831 revolutionized physics and technology.
Magnetic flux \(\Phi_B\) through a surface of area \(A\) in a magnetic field \(\vec{B}\) is:
Here, \(\theta\) is the angle between the magnetic field and the normal to the surface.
Electromagnetic induction occurs only when this flux changes with time, either by changing \(B\), area \(A\), or \(\theta\).
Whenever the magnetic flux linked with a circuit changes, an emf is induced in the circuit.
The magnitude of the induced emf \(\mathcal{E}\) in a circuit is equal to the rate of change of magnetic flux through the circuit.
For a coil with \(N\) turns:
Lenz’s law states that the direction of the induced emf (and hence current) is such that it opposes the change in magnetic flux that produced it.
This is a manifestation of the conservation of energy principle.
The negative sign indicates opposition.
Consider a conductor of length \(l\) moving at velocity \(v\) perpendicular to a uniform magnetic field \(B\). The motional emf generated is:
This emf can drive current if the conductor is part of a closed circuit.
Eddy currents are induced currents in bulk conductors when subjected to changing magnetic fields. They create magnetic fields opposing the change, causing energy loss as heat.
Eddy currents are minimized by laminating transformer cores and using magnetic materials with high resistivity.
When current in a coil changes, the changing magnetic flux through the coil induces an emf in itself opposing the change. This phenomenon is called self-induction.
Self-induced emf:
Where \(L\) is the self-inductance of the coil (in Henry, H).
Inductance depends on coil geometry, number of turns, and core material.
When the current in one coil changes, it induces emf in a nearby coil. This effect is mutual induction.
Where \(M\) is mutual inductance (Henry), and \(I_1\) is the current in the primary coil.
Energy stored in an inductor carrying current \(I\):
This energy is stored in the magnetic field created by the current.
A rotating conducting disk in a magnetic field generates emf across its radius due to motional induction.
Where \(\omega\) is angular velocity and \(R\) radius of disk.
Changing magnetic flux induces a non-conservative electric field. The emf in a closed path \(C\) is:
Unlike electrostatic fields, induced electric fields can do net work around a closed path.
Maxwell’s equations relate changing magnetic fields to induced electric fields:
| Concept | Formula | Remarks |
|---|---|---|
| Magnetic Flux | $$\Phi_B = B A \cos \theta$$ | Magnetic field \(B\), area \(A\), angle \(\theta\) |
| Faraday’s Law | $$\mathcal{E} = -N \frac{d\Phi_B}{dt}$$ | Negative sign indicates Lenz’s law |
| Motional EMF | $$\mathcal{E} = B l v$$ | Length \(l\), velocity \(v\) |
| Self-Induced EMF | $$\mathcal{E}_L = -L \frac{dI}{dt}$$ | Inductance \(L\), current change |
| Energy in Inductor | $$U = \frac{1}{2} L I^2$$ | Stored magnetic energy |
| Mutual Induction | $$\mathcal{E}_2 = -M \frac{dI_1}{dt}$$ | Mutual inductance \(M\) |
A coil of 100 turns is placed in a magnetic field perpendicular to its plane. Magnetic field changes from 0.5 T to 0.1 T in 0.02 seconds. The coil area is \(2 \times 10^{-3} \, m^2\). Find the magnitude of the induced emf.
Solution:
An inductor of inductance 0.5 H carries current of 3 A. Calculate the energy stored.
Solution:
A rod 0.2 m long moves at 5 m/s perpendicular to a magnetic field of 0.3 T. Calculate emf induced between the ends.
Solution:
The current in the primary coil changes at the rate of 20 A/s. If the mutual inductance is 0.1 H, find the induced emf in the secondary coil.
Solution:
Electromagnetic induction links magnetic fields with electric currents and plays a central role in modern electrical devices and technology. A deep understanding of Faraday's laws, Lenz’s law, inductance, and related concepts combined with consistent practice will help you excel in JEE Physics. Use this guide as a foundation to build your mastery and confidently tackle related questions in your exams.