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.
(a) Show that as the flux through the coil changes from Φ1 to Φ 2, the charge transferred through the coil will be given by Q = N(Φ 2 - Φ 1)/R, where R is the resistance of the coil and a sensitive ammeter connected across it and N is the number of turns.
(b) As a specific example, calculate B when a 100-turn coil of resistance 200 Ω and cross-sectional area 40.0 cm2 produces the following results. A total charge of 5.00 x 10-4 C 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.