Chapter 5.4, Problem 3bT

Shown at right are four Points near a positively charged rod. Points W and Y are equidistant from the rod, as are points X and Z. A charged particle with mass $m_o=3\times {10}^{-8}\text{kg}$ is released, from rest at point W and later is observed to pass point X.

1. Is the particle positively or negatively charged? Explain.

2. Suppose that the magnitude of the charge on the particle is $2\times {10}^{-6}\text{C}$ and that the speed of the particle is 40 m/s as it passes point X.

a. Find the change in kinetic energy of the particle as it travels from point W to point X.

b. Find the work done on the particle by the electric field between Point W and point X.

(Hint: See part D of section I.)

c. Find the electric potential difference between point Wand point X.

d. If the same particle were released from point Y, would its speed as it passes point Z be greater than, less than, or equal to 40 m/s? Explain.

3. Suppose that a second particle with the same mass as the first but nine times the charge (i.e., $18\times {10}^{-6}\text{C}$ ) were released from rest at point W.

a. Would the electric potential difference between points W and X change’? If so, how, if not, why not?

b. Would the speed of the second particle as it passes point X be greater than, less than, or equal to the speed of the first particle as it passed point X? Explain.

A particle with mass $m_o=3\times {10}^{-8}\text{kg}$ is launched toward the rod from point Z and turns around at point Y.

1. If the particle has charge $q_o=2\times {10}^{-6}\text{C}$, with what speed should it be launched? Explain.
2. If instead the particle has charge $9q_o\left(i.e.,18\times {10}^{-6}\text{C}\right)$ with what speed should it be launched? Explain.