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?

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 particle has charge $-5.00$ $\mu$C and mass $2.00\times {10}^{-4}$ kg. It moves from point $A$, where the electric potential is $V_A=+200$ V, to point $B$, where the electric potential is $V_B=+800$ V. The electric force is the only force acting on the particle. The particle has speed $5.00$ m/s at point $A$. What is its speed at point $B$? Is it moving faster or slower at $B$ than at $A$? Explain.

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?

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 $q_2$?