A $-9.0\text{nC}$charge sits at the origin, and a $+18\text{nC}$ charge is at $x=2.0\mathrm{cm}$. At what location(s) is the potential zero?

INT CALC Two positive point charges q are located on the y-axis at y = ±a.a. Write an expression for the electric potential at position x on the x-axis.

What is the electric potential 3.0 cm away from a $-12\text{nC}$ point charge?

A uniform electric field with strength $12\mathrm{V}/\mathrm{m}$ points from point A to point B, which are on the x-axis: $x_{\text{A}}=45\mathrm{m}$ and $x_{\mathrm{B}}=12\mathrm{m}$. What is the potential difference $V_{\text{A}}-V_{\mathrm{B}}$?

A spherical balloon is charged so that the potential on its surface is $40\mathrm{V}$. The balloon is now deflated to half its original radius (with no loss of charge). What is the new potential on its surface?

Metal sphere A is charged until it has a potential of $200\mathrm{V}$. Metal sphere B is initially uncharged, and has a radius twice the radius of sphere A. A small wire is used to connect spheres A and B, so that they form one continuous equipotential surface. What is the final potential on the surface of sphere B?

What are the strength and direction of the electric field 1.0 mm from (a) a proton and