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 248Ω 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.

Answer 1

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

                                          =   N(Φ₂ − Φ₁)/t

induced current = N(Φ₂ − Φ₁)/Rt

Q/t   =   N(Φ₂ − Φ₁)/Rt

the charge transferred through the coil, Q = N(Φ₂ − Φ₁)/R   

Given,

Q = 5.12*10^-4 C

N = 69 turns

R = 248 Ohm

Q = N(Φ₂ − Φ₁)/R

5.12*10^-4   = 69*(Φ₂ −0)/248

Φ₂ = 1.84 * 10^-3 Wb

magnetic field, B = Φ₂ / A

given, A = 42.5 m²

B = 1.84 * 10^-3/(42.5)²

B = 1.0188*10^-6 T