1) Three point charges are placed at the vertices of equilateral triangle with sides d. The charges are all positive and of magnitude Q.

a) What is the force on each charge?

b) What is the electric field at the centre of the triangle?

c) What is the electric field at the mid-point of the base of triangle?

2) Three charges are placed along a straight line at positions -d, 0, and +2d. If the charges have the values -0.2Q, Q, and q, what must be the ratio q/Q in order for the net force on charge Q to be zero?

3) Book problem 22.20.

The electric field of an electric dipole along the dipole axis is approximated by Eqns. 22-8 and 22-9. If a binomial expansion is made of 22-7, what is the next term in the expression for the dipole’s field along the dipole axis (z)? That is, what is E_Next in the folowing expression?

4) The figures below show two configurations of 2 positive and 2 negative charges with separations of order d.

a) For each configuration sketch the electric field both close to the charges (out to about 2-3d) and very far from the charges (out at >10d). (That is four sketches.)

b) Compare the two sets of figures and comment on differences and similarities.

5) a) Find the electric field at points beyond the end of a semi-infinite straight line of charge, linear density λ, lying along the negative z axis. That is, find the field at points on the positive z axis.

b) Find the potential at the same places if the source is a finite line, charge density λ, running from z = 0 to z = -D. (You can’t do this for an infinite line because you run into some interesting infinities!)

6) Book problem 22-51.

Two large parallel copper plates are a distance d apart and have a uniform electric field between them (Figure). An electron is released from the surface of the negative plate at the same time that a proton is released from the positive plate. Neglecting the force of interaction between the particles, find their distance from the positive plate when the particles pass each other.

Why do we not need to know the electric field to answer this question?

7) Book problem 22-86.

In the figure below, a uniform upward electric field of magnitude 2.00 × 10³N/C has been set up between two horizontal plates by charging the lower plate positively and the upper plate negatively. The plates have length L = 10.0cm and separation d = 2.00cm. An electron is then shot between the plates from the left edge of the lower plate. The initial velocity ₀ of the electron makes an angle θ = 45^∘ with the lower plate and has a magnitude of 6.00 × 10⁶m/s.

a) Will the electron strike one of the plates?

b) If so, which plate and how far horizontally from the left edge will the electron strike?

8) Book problem 24-22.

In the figure below a particle of charge +e is initially at the coordinate z = 20nm on the dipole axis, on the positive side of the dipole. (The origin of z is at the dipole center.) The particle is then moved along a circular path around the dipole center until it is at coordinate z = -20nm. The graph gives the work, W_a, done by the force moving the particle versus the angle θthat locates the particle. The scale is set by W_as = 4.0 × 10^-3J. What is the magnitude of the dipole moment?

9) Book problem 24-50 (altered).

A thin, spherical, conducting shell of radius R is mounted on an insulating support and charged to a potential -V ₀. An electron is then fired directly toward the center of the shell from a point P at a distance r ≫ R. What initial speed, v₀, is needed for the electron to just reach the shell before reversing direction?

10) Three equal charges, Q, are placed at the corners of an equilateral triangle of side d. There is a charge -q at the centroid of the triangle.

a) Compute the total energy needed to construct this system.

b) If the centre charge and the centroid of the triangle are held fixed, find the value of q needed to make the net force on each of the charges Q zero (so the system is in equilibrium).

c) Is the resulting system stable or unstable to small changes in d? If it is unstable, what is the ultimate fate of the system?