1. A conducting loop of area A and resistance R lies at right angles to a spatially uniform magnetic field. At time t = 0 the magnetic field and loop current are both zero. Subsequently, the current increases according to I = bt², where b is a constant with the units A/s². Find an expression for the magnetic field strength as a function of time.
2. A square wire loop of side I and resistance R is pulled with constant speed v from a region of no magnetic field until it is fully inside a region of constant, uniform magnetic field B perpendicular to the loop plane. The boundary of the field region is parallel to one side of the loop. Find an expression for the total work done by the agent pulling the loop.
3. A square wire loop 3.0 m on a side is perpendicular to a uniform magnetic field of 2.0 T. A 6-V light bulb is in series with the loop, as shown in Fig. 31-45. The magnetic field is reduced steadily to zero over a time ?t. (a) Find ?t such that the light will shine at full brightness during this time. (b) Which way will the loop current flow?
4.
5. 