MHT-CET : Physics Entrance Exam

### MHT - CET : Physics - Electomagnetic Induction Page 4

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10. Earth Coil

1. To determine horizontal and vertical component of earth's magnetic field.
2. To determine angle of dip (
d)

1. Magnetic Meridian: A vertical plane passing through the magnetic axis of a freely suspended compass needle at rest is called the magnetic meridian at that place.
2. Angle of Dip: The angle made by the earth's magnetic field with the horizontal is called the angle of dip (d) at that place. It is 0° at the magnetic equator and 90° at the poles.

If BH and Bv are horizontal and vertical components of the earth's magnetic field then

 tan d = Bv BH

 d = angle of dip

Construction:

Parts:

1. Circular coil - large number of turns wound on circular frame
2. Rectangular frame
3. Spring catch
4. Handle

Coil is free to rotate about its diameter. Spring catch allows coil to rotate rapidly through 180°.
Working:

The earth coil is connected to a ballistic galvanometer.
When coil rotates, e.m.f. is induced, given by

 e = - df dt

 \ Induced current i = e = - 1 df R R dt

 \ dq = - 1 df dt R dt

on integration, we get

 q = f1 - f2 R

The galvanometer deflects through q which is proportional to charge q passing through it.

\ q = kq

\

 kq = f1 - f2 R

...(1)

Measurement of BH:

The earth coil is set up so that
(i) its plane is perpendicular to the horizontal component of earth's magnetic field and

(ii) axis of rotation is vertical.

When coil rotates through 180°, the flux change through it is
= n ABH
- ( -n ABH) - 2nABH

 \ kq1 = 2nABH - by equation (1) R

\

 BH = ( KR ) q1 2nA

 where n = number of turns of the coil A = area of cross section of the coil R = resistance of the circuit = Resistance of the coil + resistance of the galvanometer K = constant of the galvanometer q1 = throw of the galvanometer.

Measurement of Bv:

The earth coil is set up so that
(i) its plane is perpendicular in the vertical component of earth's magnetic field and

(ii) its axis of rotation is horizontal

 Bv = ( KR ) q2 2nA

where q2 = throw of the galvanometer.

The angle of dip:

 tan d = Bv = q2 BH q1

\ d =tan-1

(

 q2 q1

)

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