Questions from Electronics

Q: A uniformly charged rod (length L, charge density λ)

A uniformly charged rod (length L, charge density λ) slides out the x axis at constant speed v. At time t=0 the back end passes the origin (so its position as a function of time is x= vt , while the f...

Q: (a) Write an expression for the volume charge density ρ

(a) Write an expression for the volume charge density ρ(r) of a point charge q at rr. Make sure that the volume integral of ρ equals q. (b) What is the volume charge density of an electric dipole, con...

Q: A particle of charge q is traveling at constant speed v along

A particle of charge q is traveling at constant speed v along the x axis. Calculate the total power passing through the plane x = a, at the moment the particle itself is at the origin.

Q: A particle of charge q1 is at rest at the origin.

A particle of charge q1 is at rest at the origin. A second particle, of charge q2, moves along the z axis at constant velocity v. (a) Find the force F12(t) of q1 on q2, at time t (when q2 is at z = vt...

Q: Develop the potential formulation for electrodynamics with magnetic charge (Eq.

Develop the potential formulation for electrodynamics with magnetic charge (Eq. 7.44). [Hint: You’ll need two scalar potentials and two vector potentials. Use the Lorenz gauge. Find the retarded poten...

Q: Find the (Lorenz gauge) potentials and fields of a time

Find the (Lorenz gauge) potentials and fields of a time-dependent ideal electric dipole p(t) at the origin.23 (It is stationary, but its magnitude and/or direction are changing with tim...

Q: Suppose / where A0, ω, and k

Suppose / where A0, ω, and k are constants. Find E and B, and check that they satisfy Maxwell’s equations in vacuum. What condition must you impose on ω and k?

Q: Which of the potentials in Ex. 10.1, Prob

Which of the potentials in Ex. 10.1, Prob. 10.3, and Prob. 10.4 are in the Coulomb gauge? Which are in the Lorenz gauge? (Notice that these gauges are not mutually exclusive.)

Q: In Chapter 5, I showed that it is always possible to

In Chapter 5, I showed that it is always possible to pick a vector potential whose divergence is zero (the Coulomb gauge). Show that it is always possible to choose / as required for the Lorenz gaug...

Q: A time-dependent point charge q(t) at the

A time-dependent point charge q(t) at the origin, ρ(r, t) = q(t)δ3(r), is fed by a current J(r, t) = −(1/4π)(q˙/r 2) rˆ, where q˙ ≡ dq/dt . (a) Check that charge is conserved, by confirming that the co...