When a non-isotropic material is heated, the fractional increase in length is different along different directions. a rectangular plate with lengths l1 = 6.1 cm and l2 = 6.0 cm is made from such a material. in the direction along l1, the coefficient of linear expansion is α1 = 10 × 10−5 k−1 . in the direction of l2, the coefficient of linear expansion is α2 = 40 × 10−5 k−1 . the plate is heated until it becomes a perfect square. what is the area of the square?

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?