What flexibility do we have in defining the vector potential given the Coulomb gauge (∇⋅A=0)? That is, what can A′ be that gives us the same B?
The vector potential A due to a long straight wire with current I along the z-axis is in the direction parallel to:
Assume the Coulomb Gauge
Consider a fat wire with radius a with uniform current I0 that runs along the +z-axis. We can compute the vector potential due to this wire directly. What is J?
Consider a fat wire with radius a with uniform current I0 that runs along the +z-axis. Given A(r)=μ04π∫J(r′)Rdτ′, which components of A need to be computed?
Consider line of charge with uniform charge density, λ=ρπa2. What is the magnitude of the electric field outside of the line charge (at a distance s>a)?
Use Gauss' Law
Consider a shell of charge with surface charge σ that is rotating at angular frequency of ω. Which of the expressions below describe the surface current, K, that is observed in the fixed frame.