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1. Magnetic flux through a plane of coil

(f) = . = BA cos q:

where

B

= magnetic induction

A

= area of the coil

q

= angle between (normal to the plane) and .

2. Induced e.m.f.:

e = -

df

dt

where e

=

e.m.f. induced in a circuit

= rate of change of flux through the circuit

negative sign indicates the direction of induced current or e.m.f.

3. e.m.f. induced in a straight moving conductor in a perpendicular magnetic field:

e = Blv

e = induced e.m.f .

B= uniform magnetic induction

l = length of the conductor

v = velocity of conductor (at right angles to the uniform magnetic induction )

4. e.m.f. induced in a metal rod rotating in a perpendicular magnetic field:

= B × p r^{2} f = BAf

B = magnetic induction

r = length of the rod

f = frequency of rotation of the rod.

5. Self induction:

(i) The flux linked with a coil is given by f = LI

L = self inductance of coil

I = current flowing through the coil

(ii) e.m.f. (self induced ) = - L

dI

= rate of change of current in the coil.

6. Mutual induction:

The magnetic flux linked with the secondary (f_{s}) is given by f_{s} = MI_{p}

M = mutual inductance

I_{p} = Current flowing in the primary coil.

e.m.f. induced in secondary = - M

dI_{p}

7. Earth coil:

(i) The angle of dip (d):

tand = Bv/B_{H}

Bv = Vertical component of earth's magnetic field

B_{H} = horizontal component of earth's magnetic field

(ii) q = k q

q = charge passing through the ballistic galvanometer

q = throw of the galvanometer

k = constant of the galvanometer

(iii) kq =

f_{1} - f_{2}

R

f_{1} - f_{2} = change in flux through the earth coil

R = Total resistance of the circuit.

(iv) Determination of B_{H} and B_{v} :

B_{H} =

(

KR

)

q_{1}

B_{v}_{ = }

q_{2}

2NA

Where B_{H} = horizontal component of earth's magnetic field B_{v} = vertical component of earth's magnetic field K = constant of the galvanometer R = resistance of the circuit N = number of turns of the coil A = area of cross-section of the coil q_{1} and q_{2} - deflection in the galvanometer (v) If the coil is quickly rotated from a_{1} to a_{2} , the induced charge is given by

q =

BnA (cosa_{1} - cosa_{2)}

where R = total resistance of the circuit containing coil. a) If the coil is rotated through an angle 90°

BnA

b) If the coil is rotator rotated through an angle 180°

2BnA