Chapter 29, Problem 68GP

A search coil for measuring B (also called a flip coil) is a small coil with N turns, each of cross-sectional area A. It is connected to a so-called ballistic galvanometer, which is a device to measure the total charge Q that passes through it in a short time. The flip coil is placed in the magnetic field to be measured with its face perpendicular to the field. It is then quickly rotated 180º about a diameter. Show that the total charge Q that flows in the induced current during this short “flip” time is proportional to the magnetic field B. In particular, show that B is given by

$B=\frac{QR}{2NA}$

where R is the total resistance of the circuit, including that of the coil and that of the ballistic galvanometer which measures the charge Q.