A flip coil is a device used to measure a magnetic field. A coil of radius r, N turns, and electrical resistance R is initially perpendicular to a magnetic field of magnitude B. The coil is connected to a special kind of galvanometer that measures the total charge Q that flows through it. To measure the field, the flip coil is rapidly flipped upside down. 

(a) What is the change in magnetic flux linkage through the coil? 

(b) If the time interval during which the coil is flipped is Δt, what is the average induced emf in the coil? 

(c) What is the average current that flows through the galvanometer? 

(d) What is the total charge Q in terms of r, N, R, and B?