Chapter 25: The Electric Potential

Proton moves along the x-axis where some arrangement of charges has produced the potential $v_x=v_0\sin (2\mathrm{\pi }/\mathrm{\lambda })$, where and l = 1.0 mm.

a. What minimum speed must the proton have at x = 0 to move down the axis without being reflected?

b. What is the maximum speed reached by a proton that at x = 0

The electron gun in an old TV picture tube accelerates electrons between two parallel plates 1.2 cm apart with a 25 kV potential difference between them. The electrons enter through a small hole in the negative plate, accelerate, then exit through a small hole in the positive plate. Assume that the holes are small enough not to affect the electric field or potential.

a. What is the electric field strength between the plates?

b. With what speed does an electron exit the electron gun if its entry speed is close to zero?

Note: The exit speed is so fast that we really need to use the theory of relativity to compute an accurate value.

Your answer to part b is in the right range but a little too big.

A room with 3.0-m-high ceilings has a metal plate on the floor with V = 0 V and a separate metal plate on the ceiling. A 1.0 g glass ball charged to +4.9 nC is shot straight up at 5.0 m/s. How high does the ball go if the ceiling voltage is (a) $+3.0\times {10}^{6}V$and (b) $-3.0\times {10}^{6}V$?

A group of science and engineering students embarks on a quest to make an electrostatic projectile launcher. For their first trial, a horizontal, frictionless surface is positioned next to the 12-cm-diameter sphere of a Van de Graaff generator, and a small, 5.0 g plastic cube is placed on the surface with its center 2.0 cm from the edge of the sphere. The cube is given a positive charge, and then the Van de Graaff generator is turned on, charging the sphere to a potential of 200,000 V in a negligible amount of time. How much charge does the plastic cube need to achieve a final speed of a mere 3.0 m/s? Does this seem like a practical projectile launcher?

Rank in order, from most positive to most negative, the potential energies$U_{\mathrm{a}}$to $U_{\mathrm{f}}$of the six electric dipoles in the uniform electric field of FIGURE Q25.5. Explain.

What is the potential energy of the electron-proton interactions in FIGURE EX25.5? The electrons are fixed and cannot move.

Two 2.0 g plastic buttons each with +50 nC of charge are placed on a frictionless surface 2.0 cm (measured between centers) on either side of a 5.0 g button charged to +250 nC.

All three are released simultaneously.

a. How many interactions are there that have a potential energy?

b. What is the final speed of each button?

What is the escape speed of an electron launched from the surface of a 1.0-cm-diameter glass sphere that has been charged to 10 nC?

An electric dipole has dipole moment p. If r W s, where

s is the separation between the charges, show that the electric

potential of the dipole can be written

$V=\frac{1}{4\mathrm{\pi }\in \circ }\frac{p\cos \theta }{r^2}$

where r is the distance from the center of the dipole and u is the

angle from the dipole axis.

Three electrons form an equilateral triangle with 1.0 nm on each side. A proton is at the center of the triangle. What is the potential energy of this group of charges?