(a) How much excess charge must be placed on a copper sphere 25.0 cm in diameter so that the potential of its center, rela­tive to infinity, is 3.75 kV? (b) What is the potential of the sphere's surface relative to infinity?

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

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. (a) 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?

Two stationary point charges +3.00 nC and +2.00 nC are separated by a distance of 50.0 cm. An electron is released from rest at a point midway between the two charges and moves along the line connecting the two charges. What is the speed of the electron when it is 10.0 cm from the +3.00-nC charge?

Two large, parallel conducting plates carrying op­posite charges of equal magnitude are separated by 2.20 cm. The surface charge density for each plate has magnitude 47.0 nC/m^2. (c) If the separation between the plates is doubled while the surface charge density is kept constant at the given value, what happens to the magnitude of the electric field and to the po­tential difference?

Two large, parallel conducting plates carrying op­posite charges of equal magnitude are separated by 2.20 cm. (a) If the surface charge density for each plate has magnitude 47.0 nC/m^2, what is the magnitude of E in the region between the plates?

An infinitely long line of charge has linear charge den­sity 5.00x10^-12 C/m. A proton (mass 1.67x10^-27 kg, charge +1.60x10^-19 C) is 18.0 cm from the line and moving directly toward the line at 3.50x10^3 m/s. (a) Calculate the proton's initial kinetic energy.

At a certain distance from a point charge, the poten-tial and electric-field magnitude due to that charge are 4.98 V and 16.2 V/m, respectively. (Take V = 0 at infinity.) (c) Is the electric field directed toward or away from the point charge?