32. Electromagnetic Waves

The magnetic field within a long, straight solenoid with a circular cross section and radius R is increasing at a rate of dB/dt. (a) What is the rate of change of flux through a circle with radius r_1 inside the solenoid, normal to the axis of the solenoid, and with center on the solenoid axis? (b) Find the magnitude of the induced electric field inside the solenoid, at a distance r_1 from its axis. Show the direction of this field in a diagram. (c) What is the magnitude of the induced electric field outside the solenoid, at a distance r_2 from the axis?

What is the magnetic field amplitude of an electromagnetic wave that has electric field amplitude $1500\text{V/m}$?

A $50\mathrm{W}$lightbulb emits light uniformly in all directions. What is the electric field amplitude $10\mathrm{cm}$away from the lightbulb?

Alice observes an electric field, $\stackrel{\rightharpoonup }{E}=(30\frac{\mathit{V}}{\mathit{m}})\widehat{\mathit{k}}$, and a magnetic field $\stackrel{\rightharpoonup }{B}=(0.10\mathit{T})\widehat{\mathit{i}}$. Bob is cruising by, with velocity $\stackrel{\rightharpoonup }{v}=(100\frac{\mathit{m}}{\mathit{s}})\widehat{\mathit{j}}$, in Alice's reference frame. What electric field does Bob observe?

The magnetic field B at all points within the colored circle shown in Fig. E29.15 has an initial magnitude of 0.750 T.

(The circle could represent approximately the space inside a long, thin solenoid.) The magnetic field is directed into the plane of the diagram and is decreasing at the rate of -0.0350 T/s. (c) What is the current in the ring if its resistance is 4.00 Ω?