In the london equation, it is postulated that the current density inside a superconductor is proportional to the vector potential, i. e., j =-aa. (a) from the london equation and the maxwell equations, derive the meissner effect. in other words, prove that the magnetic field inside a bulk superconductor is 0 when there is an applied static magnetic outside. [10] (b) now consider a superconducting plate. an external magnetic field b is applied parallel to the plate. derive the expression for b(x) inside the superconducting plate, if the plate is placed perpendicular to the x-axis.

The heater element of a 120 v toaster is a 5.4 m length of nichrome wire, whose diameter is 0.48 mm. the resistivity of nichrome at the operating temperature of the toaster is 1.3 × 10-6 ω·m. the toaster is operated at a voltage of 120 v. (a) what is the power drawn by the toaster? (b) if the cost of electricity is 12 ¢ per kilowatt-hour, and it takes 2 minutes to toast bread, how much does it cost for toasted bread? (c) when the heater element is at room temperature, is the resistivity in the nichrome wire greater than, less than, or equal to it’s resistivity when at operating temperature? explain.