Arectangular loop of wire with side lengths a and b lies in the first quadrant of the ry plane with one corner at the origin. the side along the r-axis has length a. a nonunifornm magnetic field b(y, t) =-ky3t2ż + k~5t2x, where k is a positive constant. (a) find the magnetic flux through the loop as a function of time (b) find the emf induced in the rectangular loop. (c) will the current resulting from the induced emf flow clockwise or anti-clockwise when viewed from a point in space with z > 0?

Aman does 500 j of work pushing a car a distance of 2 m. how much force does he apply? assume there is no friction. a. 250 n b. 1000 n c. 125 n d. 500 n

Ametal ball with a mass of 0.028 kg is dropped from rest at a height of 1.0 meters above the ground. assuming the energy in the ball is conserved, how much kinetic energy will the ball have when it is 0.5 meters above the ground?

Search coils and credit cards. one practical way to measure magnetic field strength uses a small, closely wound coil called a search coil. the coil is initially held with its plane perpendicular to a magnetic field. the coil is then either quickly rotated a quarter-turn about a diameter or quickly pulled out of the field. (a) derive the equation relating the total charge q that flows through a search coil 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 ∆t. the resistance of the coil is r, and the total charge is q = i∆t, 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?