## ELECTROMAGNETIC INDUCTION

Electromagnetic induction | Experiments of Faraday and Henry |

Magnetic flux | |

Faraday’s law | Statement and explanation |

Induced EMF | |

Lenz’s law | Statement |

explanation and its significance as conservation of energy | |

Motional emf | |

Eddy currents | |

Inductance | Mutual induction |

Self inductance | |

Energy stored in the coil. | |

Ac generator | Working |

Derivation of instantaneous emf in an ac generator | |

Hydro – electric generators | |

Numericals | Concept based problems |

## Magnetic flux:

The

Φ

where θ is the angle between B and A

**magnetic flux**through a surface of area A placed in a uniform magnetic field B is defined as,Φ

_{B}= B.A = BA cos θwhere θ is the angle between B and A

## Faraday’s laws of induction:

**Faraday’s laws of induction**imply that the emf induced in a coil of N turns is directly related to the rate of change of flux through it,

Here Φ

_{Β}is the flux linked with one turn of the coil. If the circuit is closed, a current I = ε/R is set up in it, where R is the resistance of the circuit.

## Lenz’s law:

**Lenz’s law**states that the polarity of the induced emf is such that it tends to produce a current which opposes the change in magnetic flux that produces it. The negative sign in the expression for Faraday’s law indicates this fact.

## Induced emf:

When a metal rod of length l is placed normal to a uniform magnetic field B and moved with a velocity v perpendicular to the field, the

ε = Blv

**induced emf (called motional emf)**across its ends is,ε = Blv

## Inductance:

**Inductance**is the ratio of the flux-linkage to current. It is equal to NΦ/I.

## Mutual inductance:

A changing current in a coil (coil 2) can induce an emf in a nearby coil (coil 1).

This relation is given by,

The quantity M

M

This relation is given by,

The quantity M

_{12}is called**mutual inductance**of coil 1 with respect to coil 2. One can similarly define M_{21}. There exists a general equality,M

_{12}= M_{21}## Self-induced emf:

When a current in a coil changes, it induces a back emf in the same coil. The

L is the

**self-induced emf**is given by,L is the

**self-inductance**of the coil. It is a measure of the inertia of the coil against the change of current through it.
The self-inductance of a long solenoid, the core of which consists of a magnetic material of relative permeability µ

L = µ

where A is the area of cross-section of the solenoid, l its length n is the number of turns per unit length.

_{r }, is given byL = µ

_{r}µ_{0}n^{2}Alwhere A is the area of cross-section of the solenoid, l its length n is the number of turns per unit length.