MHT-CET : Physics Entrance Exam

### MHT - CET : Physics - Magnetic Effect of Electric Current Page 1

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1

Tangent Galvanometer

Principle:

A magnetic needle is suspended so that two mutually perpendicular magnetic fields act on it; one due to a current carrying circular coil, and the other due to the earth's magnetic field (horizontal component BH). The needle settles in a position given by tangent law: B = BH tan q

Construction:

A T.G. consists of:

• A coil with a number of turns on a circular frame
• The frame is fixed vertically on a horizontal base
• A magnetic needle pivoted at the centre of the coil
• Pointer fixed at right angles to the needle.

Settings:

(1) The instrument is levelled so that the magnetic needle is exactly horizontal

(2) The coil is arranged in magnetic meridian.

The Two Magnetic Fields Acting on the Needle

(1) Field B due to current in the coil acts in East-West direction.

(2) Field BH, which is the horizontal component of earth's magnetic field; acts in North-South direction.

Formula

Magnetic field produced at the centre of the current careying by the coil is given by:

 B = m0 n I 2 r

where, B = magnetic field at the centre of the circular coil

I = current in the coil

n = number of turns of the coil

m0 = permeability of free space.

B = BH tan q … by tangent law

 \ m0 n I = BH tan q 2 r

 \ I = ( 2 r BH ) tan q m0 n

 K = ( 2 r BH ) is known as reduction factor. m0 n

\ I = K tan q

Sensitivity of T.G.

•  The sensitivity of a galvanometer is defined as the angle of deflection per unit current  passing through it.

 · S = d q = cos2q d I K

•  For greater sensitivity, K must be small.

 · K = 2 r BH m0 n

 \ Sensitivity increases

 if radius is reduced if effective value of BH is reduced. if number of turns are increased.

Accuracy of T.G.

 · Relative error in measurement of current I = d I I

Taking I = K tan q and differentiating,

 d I = 2 d q I sin 2 q

 · Accuracy is maximum when error is minimum. i.e., when sin 2q is maximum

 Putting maximum value of sin 2q = 1 sin 2q = 1 2q = 90° q = 45°

\

 Accuracy is maximum at q = 45°

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