Sketch the electric field for the dipole treated in our text as a snapshot in time for three consecutive times during one oscillation cycle. Explain where and why a particular field line is located in each snapshot.

(1)Derive an expression for the Lorentz force in terms of the potentials. (2) Simplify this using product rule 4 in the front of the book. 

The index of refraction decreases with altitude. Explain how an EM wave moves in this medium. 

Write dr/dt using the convective derivative. 

Derive an equation for the perpendicular component of Ei, Er, and Et at the boundary of between a conductor and air.

For a uniform magnetic field A=rxB/2. (1) derive an expression for the x component of (v dot grad) A. (2) generalize the result from (1) to all vector components.

Given the phase at - omega t at the orgin what is the phase a distance x along the x axis?

The position function of a source is xs=x0-v0t. The observer is at the origin. Derive an expression for the retarded time for xs > 0.

Derive an expression for the dipole moment of a ring in the xy plane of radius b and charge density lambda0 sin(phi).

(1) Derive an expression for the gradient of script r in the x direction. (2) Derive the full expression for the gradient of script r.

(1)Derive an expression for the gradient of the retarded charge density in the x direction. (2)Derive the full expression for this gradient.

An electron in a circular orbit decay by radiation losing power given by a0/r^4. The KE and PE of the orbiting electron is a1/r. Derive an expression for the decay time.

Evaluate the integral expression obtained in 10.10 along each path.

For problem 10.10 derive an integral expression for the vector potential.

8.6 (c) (1) sketch the path over which Faraday's law is applied. (2) Derive an expression for Faraday's law having done the line integral and using dB/dt.

8.8 (1) Sketch E and B. (2) Write an expression for the angular momentum density in terms of E and B.

8.8 (1) Apply Faraday's law to the ring shown. (2) Derive an expression for E in terms of dM/dt.

Find an expression for the dot product between the EM stress tensor and da for the xy plane between two equal charges, located at +a and -a on the z axis.

(a)Write an integral expression for conservations of cars using car current density J and lamba cars per unit length. (b) Solve this equation.

(a) Sketch the poynting vector S for the charging cap problem. (b) Calculate S at the edge of the cap.

Calculate the approximate energy stored in a cap with a>>h.