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?

Two protons, starting several meters apart, are aimed directly at each other with speeds of $2.00\times {10}^5$ m/s, measured relative to the earth. Find the maximum electric force that these protons will exert on each other.

Two protons are released from rest when they are $0.750$ nm apart. What is the maximum acceleration they will achieve and when does this acceleration occur?

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?

A point charge $q_1=+2.40$ $\mu$C is held stationary at the origin. A second point charge $q_2=-4.30$ $\mu$C moves from the point $x=0.150$ m, $y=0$ to the point $x=0.250$ m, $y=0.250$ m. How much work is done by the electric force on $q_2$?