7.3 Calculations of Electric Potential

What is the potential inside the metal sphere in the example?

What is the potential on the x-axis? The z-axis?

What is the potential on the axis of a nonuniform ring of charge, where the charge density is $\lambda \left(\theta\right) = \lambda \text{cos} \theta$ ?

Compare the electric dipole moments of charges $\pm Q$ separated by a distance d and charges $\pm Q / 2$ separated by a distance d/2.

In what region of space is the potential due to a uniformly charged sphere the same as that of a point charge? In what region does it differ from that of a point charge?

A 0.500-cm-diameter plastic sphere, used in a static electricity demonstration, has a uniformly distributed 40.0-pC charge on its surface. What is the potential near its surface?

If the potential due to a point charge is $5.00 \times 10^{2} \text{V}$ at a distance of 15.0 m, what are the sign and magnitude of the charge?

A research Van de Graaff generator has a 2.00-m-diameter metal sphere with a charge of 5.00 mC on it. Assume the potential energy is zero at a reference point infinitely far away from the Van de Graaff. (a) What is the potential near its surface? (b) At what distance from its center is the potential 1.00 MV? (c) An oxygen atom with three missing electrons is released near the Van de Graaff generat…

(a) What is the potential between two points situated 10 cm and 20 cm from a $3.0 - \mu \text{C}$ point charge? (b) To what location should the point at 20 cm be moved to increase this potential difference by a factor of two?

Two charges $–2.0 \mu \text{C} \text{and} + 2.0 \mu \text{C}$ are separated by 4.0 cm on the z-axis symmetrically about origin, with the positive one uppermost. Two space points of interest $P_{1} \text{and} P_{2}$ are located 3.0 cm and 30 cm from origin at an angle $30 °$ with respect to the z-axis. Evaluate electric potentials at $P_{1} \text{and} P_{2}$ in two ways: (a) Using the exact formula for point charges, and (b) using the approximate dipole potential formula.