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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 Then the coil is rapidly withdrawn from the field.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        q1 = Kθ1 (1 + λ/2),
Where K is the ballistic constant and λ the logarithmic decrement.
. :     NBA/R = Kθ1 (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 θ2 of the B.G., is noted.

Search coil

Let    N1 = number of turns of primary coil
    L = length of primary coil
    A1 = area of cross-section of the primary coil.

Flux linked with each turn of the secondary coil = μ0N1lxA1/l

Total flux linked with N2 turns of the secondary coil = μ0N1lN2xA1/l

When the current is reversed, the total change in flux
        = 2μ0N1N2A1/l

Induced charge    q2 = 2μ0N1N2A1/l x R

Also        q2 = Kθ2 (1 + λ/2)

. :    2μ0N1N2A1/lR = Kθ2 (1 + λ/2)                            … (2)

Dividing (1) by (2),     NBAl/2μ0N1N2A1 = θ12
        B = 2μ0N1N2A1 /NAl x θ12                         … (3)

Search coil1

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