PhysicsLAB: 2010 C3 E&M

The long straight wire illustrated above carries a current I to the right. The current varies with time t according to the equation

, where I₀ and K are positive constants and I remains positive throughout the time period of interest. The bottom of a rectangular loop of wire of width b and height a is located a distance d above the long wire, with the long wire in the plane of the loop as shown. A lightbulb with resistance R is connected in the loop. Express all algebraic answers in terms of the given quantities and fundamental constants.

	(a) Indicate the direction of the current in the loop. Justify your answer.

	(b) Indicate whether the lightbulb gets brighter, gets dimmer, or stays the same brightness over the time period of interest. Justify your answer.

	(c) Determine the magnetic field at t = 0 due to the current in the long wire at distance r from the long wire.

	(d) Derive an expression for the magnetic flux through the loop as a function of time.

	(e) Derive an expression for the power dissipated by the lightbulb.