25. Electric Potential

A small metal sphere, carrying a net charge of $q_1=-2.80$ μC, is held in a stationary position by insulat­ing supports. A second small metal sphere, with a net charge of $q_2=-7.80$ μC and mass $1.50$ g, is projected toward $q_1$. When the two spheres are $0.800$ m apart, $q_2$, is moving toward $q_1$ with speed $22.0$ m/s (Fig. E$23.5$). Assume that the two spheres can be treated as point charges. You can ignore the force of gravity. What is the speed of $q_2$ when the spheres are $0.400$ m apart?

How much work would it take to push two protons very slowly from a separation of $2.00\times {10}^{-10}$ m (a typical atomic distance) to $3.00\times {10}^{-15}$ m (a typical nuclear distance)? If the protons are both released from rest at the closer distance in part (a), how fast are they moving when they reach their original separation?

What is the electric potential energy of the group of charges in FIGURE EX25.5?

FIGURE P25.72 shows a thin rod with charge Q that has been bent into a semicircle of radius R. Find an expression for the electric potential at the center.