A 100 W lightbulb actually emits around only 10 W of light. What is the intensity of the light 1 cm away if the light is emitted perfectly spherically? What is the magnitude of the electric field emitted by the lightbulb? What about the magnetic field?

(a) When a circular parallel-plate capacitor is being charged as in Example 31–1, show that the Poynting vector $\overrightarrow{S}$ points radially inward toward the center of the capacitor, parallel to the plates.

(b) Integrate $\overrightarrow{S}$ over the cylindrical boundary of the capacitor gap to show that the rate at which energy enters the capacitor is equal to the rate at which electrostatic energy is being stored in the electric field of the capacitor (Section 24–4). Ignore fringing of $\overrightarrow{E}$.

How large an emf (rms) will be generated in an antenna that consists of a circular coil 2.2 cm in diameter having 280 turns of wire, when an EM wave of frequency 810 kHz transporting energy at an average rate of 1.0 x 10⁻⁴ W/m² passes through it? [Hint: You can use Eq. 29–4 (for a generator) because that equation can be applied to an observer moving with the generator’s coil as it rotates at ω = 2𝝅f with f the frequency of the magnetic field.]

Suppose you have a car with a 100-hp engine. How large a solar panel would you need to replace the engine with solar power? Assume that the solar panels can utilize 20% of the maximum solar energy that reaches the Earth’s surface (1000 W/m²). Explain why or why not this is practical.

A communications truck with a 44-cm-diameter dish receiver on the roof starts out 10 km from its base station. It drives directly away from the base station at 50 km/h for 1.0 h, keeping the receiver pointed at the base station. The base station antenna broadcasts continuously with 2.5 kW of power, radiated uniformly in all directions. How much electromagnetic energy does the truck's dish receive during that 1.0 h?