25. Electric Potential

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 electric dipole at the origin consists of two charges ±q spaced distance s apart along the y-axis. Find an expression for the potential V(x, y) at an arbitrary point in the xy-plane. Your answer will be in terms of q, s, x, and y.

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

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 $A$.

Which of the following instruments is used to measure voltage ($V$, electric potential difference) in a circuit?

The electric potential in a region of space is V=(150x² − 200y²)V, where x and y are in meters. What are the strength and direction of the electric field at (x, y)=(2.0 m, 2.0 m)? Give the direction as an angle cw or ccw (specify which) from the positive x-axis.

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

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.

Certain sharks can detect an electric field as weak as $1.0$ $\mu$V/m. To grasp how weak this field is, if you wanted to produce it between two parallel metal plates by connecting an ordinary $1.5$­V AA battery across these plates, how far apart would the plates have to be?

Calculate the electric potential due to a tiny dipole whose dipole moment is 4.8 x 10⁻³⁰ Cm at a point 4.1 x 10⁻⁹ m away if this point is 45° above the axis but nearer the positive charge.

Use the on-axis potential of a charged disk from Chapter 25 to find the on-axis electric field of a charged disk.

In the Bohr model of the hydrogen atom, an electron orbits a proton (the nucleus) in a circular orbit of radius 0.53 x 10^-10 m. What is the electric potential at the electron’s orbit due to the proton?

The work done by an external force to move a - 7.40 μC charge from point A to point B is 15.0 x 10^-4 J. If the charge was started from rest and had 4.82 x 10^-4 J of kinetic energy when it reached point B, what must be the potential difference between A and B?

Two large, parallel conducting plates carrying op­posite charges of equal magnitude are separated by $2.20$ cm. What is the potential difference between the two plates?

Two positive point charges q are located on the y-axis at y = ±a. Symmetry dictates that the electric field along the x-axis has only an x-component: E_y=E_z=0. Find an expression for E_x if x≪a.