Magnetic field values are often determined by using a device known as a search c

Question

Magnetic field values are often determined by using a device known as a search coil. This technique depends on the measurement of the total charge passing through a coil in a time interval during which the magnetic flux linking the windings changes either because of the motion of the coil or because of a change in the value of B. As a specific example, calculate B when a 69-turn coil of resistance 248 and cross-sectional area 42.5m2 produces the following results: A total charge of 5.12E-4C passes through the coil when it is rotated in a uniform field from a position where the plane of the coil is perpendicular to the field to a position where the coil's plane is parallel to the field.

Explanation / Answer

As, emf induced in coil = rate of change of flux * number of turns of coil

                                          =   N(2 1)/t

induced current = N(2 1)/Rt

Q/t   =   N(2 1)/Rt

the charge transferred through the coil, Q = N(2 1)/R   

Given,

Q = 5.12*10-4 C

N = 69 turns

R = 248 Ohm

Q = N(2 1)/R

5.12*10-4   = 69*(2 0)/248

2 = 1.84 * 10-3 Wb

magnetic field, B = 2 / A

given, A = 42.5 m2

B = 1.84 * 10-3/(42.5)2

B = 1.0188*10-6 T

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