FIGURE P25.70 shows a thin rod of length L and charge Q. Find an expression for the electric potential a distance x away from the center of the rod on the axis of the rod.

A very long insulating cylinder of charge of radius $2.50$ cm carries a uniform linear density of $15.0$ nC/m. If you put one probe of a voltmeter at the surface, how far from the surface must the other probe be placed so that the voltmeter reads $175$ V?

An infinitely long line of charge has linear charge den­sity $5.00\times10^{-12}$ C/m. A proton (mass $1.67\times10^{-27}$ kg, charge $+1.60\times10^{-19}$ C) is $18.0$ cm from the line and moving directly toward the line at $3.50\times10^3$ m/s. How close does the proton get to the line of charge?

FIGURE EX26.3 is a graph of E_x. What is the potential difference between x_i=1.0 m and x_f=3.0 m?

Two metal objects that are in contact must be at the same potential, an assertion we'll prove in the next chapter. Suppose a metal sphere of radius R is charged to 1000 V and a second metal sphere of radius 2R is charged to 2000 V. The two spheres are brought into contact and then separated. Afterward, what is the potential of each sphere?

A thin rod of length L and total charge Q has the nonuniform linear charge distribution λ(x)=λ₀x/L, where x is measured from the rod's left end. What is the electric potential on the axis at distance d left of the rod's left end?

A 1.0-mm-diameter ball bearing has 2.0×10⁹ excess electrons. What is the ball bearing's potential?

In a semiclassical model of the hydrogen atom, the electron orbits the proton at a distance of 0.053 nm. What is the electric potential of the proton at the position of the electron?

In a semiclassical model of the hydrogen atom, the electron orbits the proton at a distance of 0.053 nm. What is the electron's potential energy?