A ballistic galvanometer is a device that measures the total charge Q that passes through it in a short time. It is connected to a search coil that measures B (also called a flip coil) which is a small coil with N turns, each of cross-sectional area A. The flip coil is placed in the magnetic field to be measured with its face perpendicular to the field. It is then quickly rotated 180° 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

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

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QR 2NA