Chapter 30, Problem 36AP

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 coil’s motion or because of a change in the value of B. (a) Show that as the flux through the coil changes from Φ₁ to Φ₂, the charge transferred through the coil is given by Q = N(Φ₂ − Φ₁)/R, where R is the resistance of the coil and N is the number of turns. (b) As a specific example, calculate B when a total charge of 5.00 × 10⁻⁴ C passes through a 100-turn coil of resistance 200 Ω and cross-sectional area 40.0 cm² as 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 it is parallel to the field.