# Electromagnetic Induction - 3

__Fleming’s Right hand rule__:

On sleeching yours right hand’s thumb, the index finger and middle finger is such a way that thumb reresents direction of motion of conductor, the index finger ther direction of magnetic field, then the middle finger represents the direction of the induced current.

Time varying magnetic field:

If a conducting loop is placed inside a time varying magnetic field, te changing magnetic field acts as a source of electric field and hence induce an e.m.f., infact the electric field is ever induced when no conductor is present

Can be used to determine that electric field. Where is different from an electrostatic field, as it is non conservative. We cannot define the potential corresponding to this field in the usual sense, that is, dV = …. not hold hex. has … have a direction shown when is incoming because has to be negative when is positive.

__Illustration__: Consider a cylindrical magnetic field which increases with time. Find out electric field at a distance r from its centre when

(1) r < R

(2) r > R

Ans: (1) When r < R

Due to symmetry E at every part is same.

Using

=> E.2r = - r

^{2}

(for cylindrical region only)

(2) For (r > R)

Using

E.2r = - r

^{2}

__SELF INDUCTANCE__:

(1)

__First definition__:

If a coil with N turns and current I be considered.

Totl Flux = N

_{B}is directly proportional to current, that is:

N

_{B}i

The constant of this proportionality is called L (the self inductance).

(2)

__Second definition__:

I changing current in a circuit causes a change in the magnetic flux which induces E.M.F.. This E.M.F. is proprtional to the rate of chage of current. Thus

E -

__Dumb Question__: How to find potential difference across an inductor ?

Ans: We can find the direction of self induced e.m.f. across an inductor from Lenz’s law. The induced e.m.f. is produced whenever there is a change in the current in the inductor. This e.m.f. always acts to oppose this change figure shows these cases. Assume that the inductor is ideal so, V

_{a}L - V

_{a}- V

_{b}is equal to magnitude of self induced e.m.f.

__Illustration__: Find the self inductance of an ideal solenoid ?

(Assume require quantities)

Ans: For is solunoid of length l and cross sectional area. A having number of turns N, the flux linked I

_{g}is given by N.

Where is flux linked by each turn.

=> N = nlBA (n = N/l)

The magnetic induction of a solunoid is given by

B =

*µ*

_{0}nI

=> N =

*µ*n

^{2}lAI

But, N = LI

this gives LI =

*µ*

_{0}lAI

L =

*µ*

_{0}n

^{2}lA

where n = N/l = Number of turns per unit length.

__Mutual Inductance__:

A Changing current is one circuit causes a changing magnetic flux and an induced e.m.f. in a neighburing circuit.

This e.m.f. is proportional to the rate of change of current in the first circuit.

The proportionality factor is called mutual inductance.

E

_{1}

or E

_{1}= -

Also, M =

The sign is a reflection of Lenz’s law.

__Dumb Question__: What is the series and parallel combination of inductor ?

Ans: (a) In series

l

_{eff}= l

_{1}+ l

_{2}

(b) In parallel

l

_{eff}=