I'm studying the electricity and magnetism this semester at university and I am very confused by faraday's law of induction.
I understand the following case: an infinitely long wire with a changing current (quasistatic B-field approximation - the frequency is't very high)
**Ampere's law will give you the B field B = [(uo * I)/(2*pi*s)]*phi_hat
**you can then calculate the time rate of change of the flux through an imaginary rectangular area above the infinitely long wire - this is the induced EMF
**you then calculate EMF by using the potential equation. that is,
EMF = integral of electric field over the path bounding the aforementioned surface
Equating these two can lead to a solution for the induced electric field of a infinitely long wire with changing current "I(t)".
The induced E field will be parallel to the wire and has a dependence of natural log of the radial distance from the wire.
Okay, now let's consider a uniform magnetic field. Defined as
B_vec = B*z_hat
Imagine this field is changing in time, but at any given moment still uniform throughout space. You can pick a circular surface at the origin (parallel to the B-Field) and determine the induced electric field - it will be circumferential (like the B-field around a wire).
I find this perplexing because I wouldn't expect the induced electric field to depend on the coordinate system when the B-field is uniform throughout space. Is there anyone that could help me make sense of this conundrum?