Electrostatic force, field, potential energy, potential

Point charges

Problem:

Consider 3 positive charges q at the vertices of an equilateral triangle.  Each side has length l.  Find the total force on each of the charges.

Solution:

Problem:

A small negatively charged ball of mass m is suspended on a long insulating string.  An external force very slowly moves another small negatively charged ball on a horizontal path towards the first one from a large distance.  Eventually, the second ball reaches the original location of the first one.  At that moment, the first ball is elevated a small distance h above its original position.  How much work is done by the external force moving the second ball to the original location of the first one?

Solution:

Problem:

A proton is released from rest at a distance of 10-10 m from another proton.
(a)  What is the kinetic energy when the protons have moved infinitely far apart?
(b)  What is the terminal velocity of the moving proton if the other is kept at rest?  If both are free to move, what is their velocity?

Solution:

Problem:

An alpha particle containing two protons is shot directly towards a platinum nucleus containing 78 protons from a very large distance with a kinetic energy of 1.7*10-12 J.  What will be the distance of closest approach?

Solution:

Problem:

A proton is fired directly at alpha particle (He2+) such that the two particles are initially approaching one another with the same (non-relativistic) speed v0 when they are far apart.  What is the classical distance of closest approach of the two particles?

Solution:


Continuous charge distributions

Problem:

A vertical thin rod of length L carries a total charge Q uniformly distributed.  Calculate the electric field along its axis at a distance z above its top end.

Solution:

Problem:

Consider a line charge with line charge density λ = Q/2a that extends along the x-axis from x = -a to x = +a.  Find the electric field on the y-axis.

Solution:

Problem:

A disk of radius a carries a non-uniform surface charge density given by σ = σ0 r2/a2, where σ0 is a constant.
(a)  Find the electrostatic potential at an arbitrary point on the disk axis, a distance z from the disk center and express the result in terms of the total charge Q.
(b)  Calculate the electric field on the disk axis and express the result in terms of the total charge Q.
(c)  Show that the field reduces to an expected form for z >> a.
(d)  To first order in ρ, find an expression for the radial component of  E(ρ, φ, z) at a distance ρ << a away from the z-axis and evaluate it for z >> a.

Solution:

Problem:

Charge is distributed uniformly over a thin circular disk of radius R.  The charge per unit area is σ.  Calculate the electric field and potential due to the disk at a point P on the axis of the disk at a distance z away from the center.

Solution:

Similar problems


Unknown charge distributions

Problem:

The electric field in some volume V of space is  E = [2A/(x3y2) – By]i + [2A/(x2y3) – Bx]j.
(a)  Show that the line integral of this field over a close path is zero.
(b)  Which charge density ρ in the volume V is consistent with this field?

Solution: