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CISCEISC (Science) ISC Class 12
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समय सारणी१५
पाठ्यक्रम

Overview: Electromagnetic Induction

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Topics

CISCE: Class 12

Definition: Magnetic Flux

If we consider a plane perpendicular to a uniform magnetic field, then the product of the magnitude of the field and the area of the plane is called the 'magnetic flux' (Ф) linked with that plane.

CISCE: Class 12

Definition: Electromagnetic Induction

If the circuit is closed, a current flows through it. The emf and the current so produced are called 'induced emf' and 'induced current' and last only while the magnetic flux is changing. This phenomenon is known as 'electromagnetic induction'.

CISCE: Class 12

Definition: Motional emf

When a straight conductor of length 1 moves with a velocity v perpendicular to a magnetic field B an emf (or PD) is developed across the ends of the conductor which is known as motional emf (or PD) given by V = Bvl.

CISCE: Class 12

Definition: Self-Induction

The phenomenon of electromagnetic induction in which, on changing the current in a coil, an opposing induced emf is set up in that very coil is called self-induction. The induced emf is called 'back emf'.

CISCE: Class 12

Definition: Coefficient of Self-Induction

The coefficient of self-induction of a coil is equal to the number of flux-linkages with the coil when unit current is flowing through the coil.

CISCE: Class 12

Definition: Henry

One henry is the inductance of a circuit in which an emf of 1 volt is induced when the current changes at the rate of 1 ampere per second.

CISCE: Class 12

Definition: Mutual Induction

If we place two coils near each other and pass electric current in one of them, or change the current already passing through it, or stop the current, then an emf is induced in the second coil. This phenomenon of electromagnetic induction is called 'mutual induction'.

CISCE: Class 12

Definition: Coefficient of Mutual Induction

The coefficient of mutual induction of two coils is equal to the number of magnetic flux-linkages in one coil (secondary coil) when a unit current flows in the 'other coil' (primary coil).

CISCE: Class 12

Definition: Eddy Currents

Eddy currents (or Foucault currents) are the induced currents set up throughout the volume of a conductor when the magnetic flux linked with it changes.

CISCE: Class 12

Formula: Magnetic Flux

Ф = (В сos θ) A = BA cos θ

SI units: weber
Dimensions: [ML2T-2A-1]

CISCE: Class 12

Formula: Induced emf

e = \[-N\frac{\Delta\Phi_{B}}{\Delta t}\]

CISCE: Class 12

Formula: Induced Current

I = \[\frac{e}{R}=\frac{N}{R}\frac{\Delta\Phi_B}{\Delta t}\]

CISCE: Class 12

Formula: Charge Flow During Electromagnetic Induction

q = \[I\times\Delta t=\frac{N}{R}\frac{\Delta\Phi_{B}}{\Delta t}\times\Delta t\] = \[\frac{N}{R}\Delta\Phi_B\]
= \[\frac{\text{number of turns}\times\text{change in magnetic flux}}{\text{resistance}}\]

CISCE: Class 12

Formula: Self-Induction

L = \[\frac{N\Phi_B}{I}\]

CISCE: Class 12

Formula: Coefficient of Self-Induction

L = \[-\frac{e}{\Delta I/\Delta t}\]

Units: \[\frac{\mathrm{newton}\times\mathrm{metre}\times\mathrm{second}}{\mathrm{coulomb}\times\mathrm{ampere}}\]

Dimensions: [M L2 T-2A-2].

CISCE: Class 12

Formula: Self-Inductance of a Long Solenoid

L = \[\frac{\mu N^2A}{l}=\frac{\mu_r\mu_0N^2A}{l}\]

CISCE: Class 12

Formula: Energy Stored in an Inductor

\[U=\frac{1}{2}LI_0^2\]

CISCE: Class 12

Formula: Energy Density

Energy Density = \[\frac {U}{V}\] = \[\frac {1}{2}\]\[\frac {B^2}{μ_0}\]

CISCE: Class 12

Formula: Coefficient of Mutual Induction

M = \[-\frac{e_{2}}{\Delta I_{1}/\Delta t}\]

SI units = 'henry' (H) = 1 H = 1V s A-1 = 1 Wb A-1.

CISCE: Class 12

Law: Lorentz Force Law

Statement

When a conducting rod moves in a uniform magnetic field, the charges in it experience a magnetic force (Lorentz force) and a potential difference (motional emf) is produced across its ends. The induced potential difference (motional emf) is given by

V = Bvl

when a straight conductor of length l moves with velocity u perpendicular to a magnetic field B.

Explanation / Proof

  • A conducting rod JK of length l is placed in a uniform magnetic field B (perpendicular to the plane) and moved with constant velocity v perpendicular to its axis.

  • A charge qqq moving with velocity v in magnetic field B experiences a magnetic force of magnitude
    Fm = qvB
    This force is called the Lorentz force and acts perpendicular to both B and v.

  • Due to this force, electrons move toward end K, making J positive and K negative, so a potential difference V is produced and an electric field E is set up in the rod with magnitude
    E = \[\frac {V}{l}\]   ...(i)
    The electric field exerts an electric force on charge qqq of magnitude
    Fe = qE

  • Electrons keep moving until the electric force balances the magnetic force:
    Fe = Fm ⇒ qE = qvB ⇒ E = Bv...(ii)

  • Comparing (i) and (ii):
    \[\frac{V}{l}=Bv\Rightarrow V=Bvl\]

Conclusion

The induced potential difference across the ends of a straight conductor moving with velocity v perpendicular to a magnetic field B is

V = Bvl

This induced potential difference is called motional emf.

CISCE: Class 12

Key Points: Methods of Changing the Magnetic Flux

  • The magnetic flux through a coil in a uniform magnetic field is
    Φ = BA cos ⁡θ,where θ is the angle between the area vector and the magnetic field.
  • Magnetic flux can be changed by rotating the coil, i.e., by changing θ; the induced emf then depends on the angular velocity of rotation.
  • Magnetic flux can also be changed by changing the area A of the coil within the field or by changing the magnetic field B, both of which produce an induced emf.
CISCE: Class 12

Key Points: Eddy Currents

  • Eddy currents flow inside a metal when the magnetic flux linked with it changes, and they always oppose the change.
  • Eddy currents can be very strong and cause metal heating, leading to energy loss.
  • Their strength decreases when the metal's resistance is high.
  • In motors and transformers, eddy currents are reduced by using laminated iron cores to minimise heating losses.
  • Eddy currents are useful in damping of instruments, induction furnaces, induction motors, electric brakes, and speed-measuring devices.
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