25. Electric Potential

Two equal positive point charges are placed at different distances from each other. Which configuration has more electric potential energy: when the charges are closer together or farther apart? $U=\frac{k{q}_1{q}_2}{r}$

Given three point charges, $q_1$, $q_2$, and $q_3$, located at the vertices of a triangle with distances $r_{12}$, $r_{13}$, and $r_{23}$ between them, what is the total electric potential energy of the system?

For an electric dipole placed in a uniform external electric field, what orientation of the dipole corresponds to the greatest electric potential energy ($U=\; -pEcos(\theta )$)?

If a charge of $1c$ is moved by the electric force from point $a$ to point $b$, what is the work done by the electric force?

If two parallel conducting surfaces are separated by a distance $d$ and a potential difference $V$ is applied between them, what is the expression for the distance $d$ in terms of the electric field $E$ and the potential difference $V$?

An electron moves from point i, where the electric potential is $V{i}_{}$, to point f, where the electric potential is $V{f}_{}$. How does the electric potential energy of the electron change as it moves from i to f?

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.

You are given the equation(s) used to solve a problem. Finish the solution of the problem: (9.0×10⁹Nm²/C²)q₁q₂/0.030m =90×10⁻⁶J; q₁+q₂=40nC.