25. Electric Potential

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?

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 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?

What is the electric potential at the point indicated with the dot in FIGURE EX25.31?

A 2.0-mm-diameter glass bead is positively charged. The potential difference between a point 2.0 mm from the bead and a point 4.0 mm from the bead is 500 V. What is the charge on the bead?

The potential 1.0 cm from the surface of a metal sphere is 8000 V. The potential 3.0 cm from the surface is 4000 V. What is the radius of the sphere?

Two spherical drops of mercury each have a charge of 0.10 nC and a potential of 300 V at the surface. The two drops merge to form a single drop. What is the potential at the surface of the new drop?

Two point charges qₐ and qᵦ are located on the x-axis at x=a and x=b. FIGURE EX25.36 is a graph of V, the electric potential. What is the ratio |qₐ/qᵦ|?

Charge is uniformly distributed with charge density ρ inside a very long cylinder of radius R. Find the potential difference between the surface and the axis of the cylinder.

Which point in FIGURE EX26.5, A or B, has a larger electric potential?

The electric field in a region of space is E_x=5000x V/m , where x is in meters. Find an expression for the potential V at position x. As a reference, let V=0 V at the origin.