# Electric Potential

Physics 210: Problem Set 3
Due Date: February 14, 2020
1. A charge of 4.8 × 10−19 C is separated from another point charge of −4.8 × 10−19 C by a
distance of 6.4×10−10 m. What is the electric potential of a point that is 9.2×10−10 m from
both charges?
2. A positive point charge +Q is located on the x-axis at x = −a. (a) How much work is needed
to bring a second charge +Q from infinity to x = a? (b) With 2 charges Q at x = ±a, how
much work is needed to bring a charge −Q from infinity to x = 0? (c) How much work is
needed to bring the −Q charges from x = 0 to x = 2a along the semicircular path shown
below.
3. Consider the following model the hydrogen atom. A small point change of +q is surrounded
by a uniform spherical distribution of negative charge with constant charge density ρ and
radius, r0. Using the fact that hydrogen atom is neutral, find ρ0 in terms of q and r0. (b) Find
the potential at any distance r from the center.
4. A particle of mass m and charge +q is constrained to move along the x-axis. At x = −L
and x = L, there are two rings of radius L, each with charge +Q distributed uniformly. (a)
Find V(x) along the x-axis due the charges on the rings. (b) Show V(x) has a minimum at
x = 0 (c) Show that for x  L that V (x) ≈ V (0) + αx2
and find α. (d) Find the angular
frequency of the particle if it is slightly displaced from the origin. For part (d), you might
want to recall that the potential energy of a spring is 1
2
kx2 =
1
2mω2x
2
5. Show that the total work to assemble (from infinity) an uniformly charged sphere of radius
R and total charge Q is given by 3Q2/(20π0R). Hint: Energy conservation says that the
1
energy to make the sphere is equal to its electrostatic energy. The electrostatic potential
energy is U =
R
V (q)dq. Now for the sphere we must determine how we want to integrate
in q.
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