Suppose a spherical capacitor is being charged. In this case the E field between the plates is growing with time which implies a displacement current which in turn implies a B field. How would one find this B field if it does exists? I'm guessing the B field is zero because of symmetry. I...
On page 317 of "INTRODUCTION TO ELECTRODYNAMICS" 4th Ed. by Griffiths he states without proof that the analog to Biot-Savart for finding the E field is:
Can anyone direct me to a reference where this is proved or give me a hint how to prove it? Thank you.
After further work and thinking about your responses with respect to finding the E field given a uniform B(t) field in the z-direction using Faraday's Law, I have come up with following:
∇×E=−∂B(t)/∂t (Faraday's Law in differential form)
One solution is E = <−yβ/2,xβ/2,0> where β =...
Thank you Mr. Link for your patience. I'm sorry to say I'm still a bit confused and perhaps it can be cleared up by an answer to the following question:
With a single uniform, time dependent B(t) field point in the z direction (i.e., the B(t) is everywhere perpendicular to the xy plane). And...
Thank you for the response. In my thought experiment there are only two imaginary loops which intersect at two points (no wires, thus no currents) thus only E fields in space. Basic question was how can here be two different E fields at the common point P where the circles intersect.
Thank you for your response which I understand. However, this leads to other questions: (1) is there a perpendicular component of E due to the changing flux and (2) if so, how would I find it using Faraday's law?
I'm confused by an apparent ambiguity in the direction the E field in Faraday's law:
∫ E°dl = - ∂/∂t ∫ B°da
Faraday's law says the change in magnetic flux through an open surface gives rise to an emf equal to E°dl taken around the closed loop which is the boundary of the open surface.
And...