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 $A$.

Two stationary point charges $+3.00$ nC and $+2.00$ nC are separated by a distance of $50.0$ cm. An electron is released from rest at a point midway between the two charges and moves along the line connecting the two charges. What is the speed of the electron when it is $10.0$ cm from the $+3.00$-nC 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 $B$.

Two point charges of equal magnitude $Q$ are held a distance $d$ apart. Consider only points on the line passing through both charges. If the two charges have the same sign, find the location of all points (if there are any) at which (i) the potential (relative to infinity) is zero (is the electric field zero at these points?), and (ii) the electric field is zero (is the potential zero at these points?).

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?

Point charges $q_1=+2.00$ $\mu$C and $q_2=-2.00$ $\mu$C are placed at adjacent corners of a square for which the length of each side is $3.00$ cm. Point $a$ is at the center of the square, and point $b$ is at the empty corner closest to $q_2$$q_2$. Take the electric potential to be zero at a distance far from both charges. (a) What is the electric potential at point a due to $q_1$ and $q_2$?