## Search Coil Method

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# Search-coil Method of measuring Magnetic Field Induction

The experimental arrangement for measuring field between the pole-pieces of a strong magnet. The search coil C is placed in the gap between the pole-pieces with its plane normal to the field. It is connected in series with a B.G., and secondary coil S of a solenoid. The primary coil P is connected through a reversing-key K to a battery, an ammeter A and a rheostat. Initially the primary circuit is kept off.Supposed B is the magnetic field induction. A the area of cross-section of each turn of the search coil in NBA. Then the coil is rapidly withdrawn from the field. Thus the magnetic flux changes by NBA. The first throw θ1 of the B.G., due to the induced charge is noted.

Let R be the resistance of the secondary circuit. Then, the induced charge q1 = NBA/R

Also q

_{1}= Kθ

_{1}(1 + λ/2),

Where K is the ballistic constant and λ the logarithmic decrement.

. : NBA/R = Kθ

_{1}(1 + λ/2) … (1)

In order to determine K, a known current I flowing through the primary P is reversed using the reversing key. The corresponding throw θ

_{2}of the B.G., is noted.

Let N

_{1}= number of turns of primary coil

L = length of primary coil

A

_{1}= area of cross-section of the primary coil.

Flux linked with each turn of the secondary coil = μ

_{0}N

_{1}lxA

_{1}/l

Total flux linked with N2 turns of the secondary coil = μ

_{0}N

_{1}lN

_{2}xA

_{1}/l

When the current is reversed, the total change in flux

= 2μ

_{0}N

_{1}N

_{2}A

_{1}/l

Induced charge q

_{2}= 2μ

_{0}N

_{1}N

_{2}A

_{1}/l x R

Also q

_{2}= Kθ

_{2}(1 + λ/2)

. : 2μ

_{0}N

_{1}N

_{2}A

_{1}/lR = Kθ

_{2}(1 + λ/2) … (2)

Dividing (1) by (2), NBAl/2μ

_{0}N

_{1}N

_{2}A

_{1}= θ

_{1}/θ

_{2}

B = 2μ

_{0}N

_{1}N

_{2}A

_{1}/NAl x θ

_{1}/θ

_{2}… (3)

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