Here students can locate TS Inter 2nd Year Physics Notes 9th Lesson Electromagnetic Induction to prepare for their exam.

## TS Inter 2nd Year Physics Notes 9th Lesson Electromagnetic Induction

→ Faraday and Henry experiments & con-clusions.

- It is the relative motion between the magnet and the coil that is responsible for genera¬tion of electric current in a coil.
- The motion of a coil towards a stationary magnet or motion of a magnet towards a stationary coil will produce the same effect.
- The direction of current produced when magnet is taken away from coil or coil is taken away from magnet is opposite to that of current produced when magnet is appro-aching the coil or coil is approaching the magnet.
- If a steady current is passed through one coil and another coil is brought nearer to it then it is the relative motion between the coils that induces the electric current.

→ Magnetic flux: The number of magnetic field lines crossing unit area when placed normal to the field at that point is defined as “magnetic flux”.

Magnetic flux, Φ = B̅. A̅ = B A cos 0

Note: The concept of magnetic flux in magnetism is similar to volume flux of a liquid in Hydrostatics.

→ Faraday’s law of Induction:

The time rate of change of magnetic flux through a circuit induces emf in it.

Induced emf, ε = –\(\frac{d \phi_{\mathrm{B}}}{\mathrm{dt}}\)

If there are ‘N’ turns in the coil then = -N \(\frac{d \phi_{\mathrm{B}}}{\mathrm{dt}}\)

→ Lenz’s law: The polarity of induced emf is such that it tends to produce a current which opposes the change in magnetic flux that produces current in that coil.

Note:

- When North pole is brought near to a coil North pole is induced in the coil facing North pole.
- When South pole is brought near to a coil South pole is induced in the coil facing that South pole.

→ Motional emf: When a straight conductor is moving through a uniform and time independent magnetic field then emf is induced across that conductor.

Induced emf, ε = B/v

→ Energy consideration of motion of a conductor in a magnetic field: When a conductor of resistance Vand length T is moving in a magnetic field B then

Induced emf, ε = B/v; current I = \(\frac{\mathrm{B} l \mathrm{v}}{\mathrm{r}}\)

Force on a charged condutor F = I/B = \(\frac{\mathrm{B}^2 l^2 \mathrm{v}}{\mathrm{r}}\)

Power associated with motioi jf wire P = F × v = B^{2}I^{2}v^{2} /r

→ Eddy currents: When large pieces of con-ductors are subjected to changing magne-tic flux then current is induced in them. These induced currents are called “Eddy currents”.

Eddy currents will oppose the motion of the coil or they oppose the change in magnetic flux.

Eddy currents can be minimised by using laminations of metal to make a metal core with a dielectric seperation between them. Ex: Core of transformer.

→ Some applications of eddy currents are

- Magnetic breaking of trains
- Electro-magnetic damping of oscillations
- Induction furnace and
- Electric power motors.

→ Inductance:

The process of producing emf in a coil due to changing current in that coil or in a coil near by it is called Inductance.

Flux associated with a coil Φ_{B} is proportional to current i.e., Φ_{B} ∝ I

Rate of change in flux \(\frac{d \phi_B}{d t} \propto \frac{d I}{d t}\) or \(\frac{\mathrm{d} \phi_{\mathrm{B}}}{\mathrm{dt}}\) = constant.\(\frac{\mathrm{dl}}{\mathrm{dt}}\)

This constant of proportionality is called Inductance.

Note:

- Inductances are of two types
- Self inductance (L),
- Mutual inductance (M)

- Inductance is a scalar quantity; S.I. unit: Henry; Dimensions ML
^{2}T^{-2}A^{-2}

→ Self inductance (L): If emf is induced in a single isolated coil due to change of flux in that coil by means of changing current through that coil then that phenomenon is called “Self inductance L”.

In Self inductance, ε = -L\(-\frac{\mathrm{dI}}{\mathrm{dt}}\)

Its SI unit is henry (H)

Note: The rate of self inductance in electromagnetism is similar to inertia in mechanics.

→ Mutual inductance (M): The phenomenon of inducing emf in one coil due to changing magnetic flux in other coil is called “Mutual inductance (M)”.

Mutual Induced emf, ε = -M\(\left(\frac{\mathrm{di}}{\mathrm{dt}}\right)\)

→ AC Generators: In AC generators induced emf or current in loop changes with the orientation of loop between two magnetic poles.

i.e., In AC generator a coil of area (A) is rotated in a stationary magnetic field (B) with some mechanical arrangement.

Flux linked Φ = BA cos θ per loop, or Φ = NBA cos θ for a coil of N turns, where θ = ωt

Induced emf, ε = -N\(\frac{\mathrm{d} \phi_{\mathrm{B}}}{\mathrm{dt}}\) = -NBA\(\frac{\mathrm{d}}{\mathrm{dt}}\)(cos θ)

or ε = – NBA ωsin ωt OR ε = – NBA to sin ωt

The term NBAω is also called ε_{max}

Types of AC generators:

- Hydro-electric generators: In an AC generator if the coil is rotated in magnetic field with the mechanical power pro¬duced by water then it is called Hydroelectric generator.
- Thermal generators: In this type of AC generators energy necessary to rotate the coil in magnetic field is obtained by heating water with coal or some other sources like gas or furnace oil.
- Nuclear generators: In this type of AC generators energy necessary to rotate the coil in magnetic field is obtained by heating water with nuclear fuel.

→ Magnetic flux, Φ = B̅ .A̅ = B A cos θ

Where ‘θ’ is the angle between B̅ and A̅.

→ Induced emf ε = \(\frac{-\mathrm{d} \phi_{\mathrm{B}}}{\mathrm{dt}}\) for a loop of one turn

(OR) ε = -N\(\frac{-\mathrm{d} \phi_{\mathrm{B}}}{\mathrm{dt}}\) for a coil of N turns

→ Motional emf of a conductor in magnetic field ε = \(\frac{-\mathrm{d} \phi_{\mathrm{B}}}{\mathrm{dt}}\) = -Bl\(\frac{\mathrm{dx}}{\mathrm{dt}}\) = -B/V dt

ε = Blv

→ Current in the wire, I = \(\frac{\varepsilon}{\mathrm{r}}=\frac{-\mathrm{B} l \mathrm{v}}{\mathrm{r}}\), where ‘r’ is the resistance of wire

→ Force on the conductor, F = IlB = \(\frac{\mathrm{B}^2 l^2 \mathrm{v}}{\mathrm{r}}\)

→ Power associated with the motion P = Fv = IlBV = B^{2}I^{2}V^{2}/r

→ Mutual Inductance M = μ_{0}n_{1}n_{2}πr_{1}^{2}l

Energy stored in a coil W = \(\frac{1}{2}\)Li^{2}

→ AC Generators:

- Angular displacement of coil θ = ωt ω = Angular velocity of coil
- Flux linkage with coil Φ
_{B}= B̅ .A̅ = B A cos θ = BA cos ωt - Induced emf, ε = -N\(\frac{\mathrm{d} \phi_{\mathrm{B}}}{\mathrm{dt}}\) = NBAω sin ωt
- Maximum emf induced, ε
_{m}= NBAω - emf. at any time, ε = ε
_{max}sinωt = ε_{max}sin(2πυt)

where υ is frequency of rotation.