5.1.1. In a source-free region, we find that B = zu _y + x u _z. Does E vary with time?

5.1.2. A perfect conductor joins two ends of a 100 ? resistor, and the closed loop is in a region of uniform magnetic flux density B = 10 e ^{(- t /10)} T.

Neglecting the self-inductance of the loop, find and plot the voltage V( t) that appears across the 100 ? resistor. A device based on this principle is used to monitor time-varying magnetic fields in experiments and in biological studies.

5.1.3. A closed loop ( ? x = 30 cm ? y = 20 cm) of wire passes through a nonuniform time-independent magnetic field B = y u _z T with a constant velocity v ₀ = 5 u _x m/s. At t = 0, the loop's lower left corner is located at the origin. Find an expression for the voltage V, generated by the loop as a function of time. You may neglect the magnetic field created by the current in the loop.

5.1.4. Repeat Problem 5.1.3 with the magnetic flux density being uniform in space B = 0.1 u _z T. Explain your result.

5.1.5. Find the generated voltage if the axle moves at a constant velocity v = v u