At a certain distance from a point charge, the potential and electric-field magnitude due to that charge are $4.98$ V and $16.2$ V/m, respectively. (Take $V=0$ at infinity.) What is the magnitude of the charge?

Two point charges $q_1 = +2.40$ nC and $q_2 = -6.50$ nC are $0.100$ m apart. Point $A$ is midway between them; point $B$ is $0.080$ m from $q_1$ and $0.060$ m from $q_2$ (Fig. E$23.19$). Take the electric potential to be zero at infinity. Find the potential at point $B$.

At a certain distance from a point charge, the potential and electric-field magnitude due to that charge are $4.98$ V and $16.2$ V/m, respectively. (Take $V = 0$ at infinity.) What is the distance to the point charge?

An electron is to be accelerated from $3.00\times {10}^6$ m/s to $8.00\times {10}^6$ m/s. Through what potential difference must the electron pass to accomplish this?

A thin spherical shell with radius $R_1=3.00$ cm is concentric with a larger thin spherical shell with radius $R_2=5.00$ cm. Both shells are made of insulating material. The smaller shell has charge $q_1=+6.00$ nC distributed uniformly over its surface, and the larger shell has charge $q_2=-9.00$ nC distributed uniformly over its surface. Take the electric potential to be zero at an infinite distance from both shells. What is the electric potential due to the two shells at the following distance from their common center: (i) $r=0$; (ii) $r=4.00$ cm; (iii) $r=6.00$ cm?

An infinitely long line of charge has linear charge den­sity $5.00\times {10}^{-12}$ C/m. A proton (mass $1.67\times {10}^{-27}$ kg, charge $+1.60\times {10}^{-19}$ C) is $18.0$ cm from the line and moving directly toward the line at $3.50\times {10}^3$ m/s. Calculate the proton's initial kinetic energy.

At a certain distance from a point charge, the potential and electric-field magnitude due to that charge are $4.98$ V and $16.2$ V/m, respectively. (Take $V = 0$ at infinity.) Is the electric field directed toward or away from the point charge?