Question

If we move a refrigerator magnet back and forth, we generate an electromagnetic wave that propagates away from us. Assume we move the magnet along the z-axis centered on the origin with an amplitude of 10 cm and with a frequency of 2.0 Hz. Consider a loop in the xy-plane centered on the origin with a radius of 2.0 cm. Assume that when the magnet is closest to the loop, the magnetic field within the loop has a spatially uniform value of 0.010 T. When the magnet has moved 10 cm in the direction away from the loop, the field in the loop becomes negligible.

Calculate the average rate at which the magnetic flux through the loop changes in time during each half-cycle of the motion of the magnet.

Use Faraday's law to estimate the average magnitude of the induced electric field at points on the loop.

Use the equation S⃗ =1μ0E⃗ ×B⃗ S→=1μ0E→×B→ to estimate the average intensity of the electromagnetic wave in the xyxy-plane as it propagates radially away from the zz-axis a distance of 2.0 cmcm.

Assume the intensity has the same value along the surface of a cylinder centered on the zz-axis that extends 5.0 cmcm above and 5.0 cmcm below the xyxy-plane and is negligible above or below this. (We are crudely postulating that the wave is emitted perpendicular to the axis of the motion in a narrow band.) Use this assumption to estimate the total power dissipated by the wave.

Answer 1