- #1

- 18

- 4

∫ 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 also says the induced E field around the loop exists even if there is not an actual wire loop to support current flow.

My understanding is that E is always parallel to dl around the closed loop. This is supported by:

(1) The Walter Lewin MIT lecture at

at time 20:22 into the lecture where he says "E and dl are always in the same direction if you stay in the wire."

(2) Also Example 7.7, page 306 of "Introduction to Electrodynamics, 3th ed." by David Griffiths which implies E is parallel to dl.

Here is a simple example of the ambiguity involving two intersecting loops which are circles in the xy plane and a B(t) field perpendicular to the xy plane:

(1) Let a time variable uniform B(t) field be everywhere perpendicular to the xy plane.

(2) Let C1 be a circle in the xy plane where the associated flux surface is the area enclosed by C1 in the xy plane.

(3) Likewise, let C2 be another circle in the xy plane where the associated flux surface is the area enclosed by C2 in the xy plane.

(4) In addition, C1 and C2 intersect where P is one point of intersection.

(5) Applying Faraday's law to both circles we see an E tangent to C1 at P and also a different E tangent to C2 at P. Thus two E vectors at the same point in the xy plane, each pointing in a different directions in the xy plane. How can this be?

Please point out my error in this analysis.