(a) derive the equation relating the total charge q that flows through a search coil (conceptual example 29.3) to the magnetic-field magnitude b. the search coil has n turns, each with area a, and the flux through the coil is decreased from its initial maximum value to zero in a time δt. the resistance of the coil is r, and the total charge is q=iδt, where i is the average current induced by the change in flux.
(b) in a credit card reader, the magnetic strip on the back of a credit card is rapidly "swiped" past a coil within the reader. explain, using the same ideas that underlie the operation of a search coil, how the reader can decode the information stored in the pattern of magnetization on the strip.(c) is it necessary that the credit card be "swiped" through the reader at exactly the right speed? why or why not?