Field Transformations: loop moving along wire

[Rose Garden]

Homework Statement

A loop moves with velocity v along a charged wire. (The charged wire passes through the center of the loop.)

In a reference frame where the charged wire is stationary and the loop is moving with v, what is the E field and B field at a point on the loop?

In a reference frame where the charged wire is moving with -v and the loop is stationary, what is the E field and B field at a point on the loop?

Homework Equations

E'= E + V x B
B' = B - (1/c^2)V x E

The Attempt at a Solution

When the charged wire is stationary and the loop is moving with v, is the E equal to the E of a point from a charged wire plus the cross product of velocity and the magnetic field B' (the B' in ref frame where wire is moving and a current does exist)?
That is E = $$\lambda$$/(2$$\pi$$$$\epsilon$$r) + V x B' ...where lamda is charge density of the wire, and where B'=$$\mu$$I/(2$$\pi$$r)
And is the B simply 0 because there is no current?

p.s. sorry don't know why latex is doing that but there's no superscripts in the equations

 

[member 553083]

Yes, when the charged wire is stationary and the loop is moving with velocity v, the E field at a point on the loop is equal to the E field from a charged wire plus the cross product of velocity and the magnetic field B'. The B field at this point is simply 0 since there is no current.When the charged wire is moving with velocity -v and the loop is stationary, the E field at a point on the loop is equal to the E field from a charged wire plus the cross product of velocity and the electric field E'. The B field at this point is equal to the B field from a current carrying wire minus the cross product of velocity and the electric field E'.