A proton is fired with a speed of 1.0×10⁶ m/s through the parallel-plate capacitor shown in FIGURE P31.29. The capacitor's electric field is E =(1.0×10⁵ V/m, down). How does an experimenter in the proton's frame explain that the proton experiences no force as the charged plates fly by?

Unpolarized light with intensity 350 W/m² passes first through a polarizing filter with its axis vertical, then through a second polarizing filter. It emerges from the second filter with intensity 131 W/m². What is the angle from vertical of the axis of the second polarizing filter?

What is the force (magnitude and direction) on the proton in FIGURE P31.28? Give the direction as an angle cw or ccw from vertical.

In FIGURE P31.32, a circular loop of radius r travels with speed v along a charged wire having linear charge density λ. The wire is at rest in the laboratory frame, and it passes through the center of the loop. What electric and magnetic fields would an experimenter in the loop's frame calculate at distance r from the current of part c?

FIGURE EX31.23 shows a horizontally polarized radio wave of frequency 1.0×10⁶ Hz traveling into the figure. The maximum electric field strength is 1000 V/m. What is the maximum magnetic field strength?

A simple series circuit consists of a 150 Ω resistor, a 25 V battery, a switch, and a 2.5 pF parallel-plate capacitor (initially uncharged) with plates 5.0 mm apart. The switch is closed at t = 0 s. Find the electric flux and the displacement current at t = 0.50 ns.

An electron travels with $\vec{v}=(5.0\times {10}^6\hat{i})\text{m/s}$ through a point in space where $\vec{E}=(2.0\times {10}^5\hat{i}-2.0\times {10}^5\hat{j})\text{V/m}$ and $\vec{B}=-0.10\hat{k}\text{T}$. What is the force on the electron?