13.6 Exercise 5

A flip coil is a relatively simple device used to measure a magnetic field. It consists of a circular coil of N turns wound with fine conducting wire. The coil is attached to a ballistic galvanometer, a device that measures the total charge that passes through it. The coil is placed in a magnetic field $\overset{\rightarrow}{B}$ such that its face is perpendicular to the field. It is then flipped through $180 ° ,$ and the total charge Q that flows through the galvanometer is measured. (a) If the total resistance of the coil and galvanometer is R, what is the relationship between B and Q? Because the coil is very small, you can assume that $\overset{\rightarrow}{B}$ is uniform over it. (b) How can you determine whether or not the magnetic field is perpendicular to the face of the coil?