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## Main Question or Discussion Point

Assume that I am having a 3D Cartesian Coordinate and a linearly time-dependent magnetic field ##\textbf{B}(t) = B_0 \cdot k \cdot t \cdot \textbf{z}## where ##B_0## and ##k## are just constants.

If circular conductor(a thin ring whose thickness is negligible) is put parallel to the ##XY## plane and one measures the voltage difference on 2 different points ##a, b##, how shall I predict which one will have a higher voltage?

What confuses me is that according to Faraday's Law, the electric field around the circular conductor is given by

##\nabla \times \textbf{E} = - \frac{\partial \textbf{B}}{\partial t}##

Thus for any point on the conductor the induced electric field is the same. Then going from any point along the induced electric field till reaching the same point one gets a voltage drop. For any 2 different points ##a, b## on the circular conductor I can always go from ##b## to ##a## or from ##a## to ##b## "along the induced electric field" and get voltage drops for both cases.

Could any one help to resolve the part that confuses me?

If circular conductor(a thin ring whose thickness is negligible) is put parallel to the ##XY## plane and one measures the voltage difference on 2 different points ##a, b##, how shall I predict which one will have a higher voltage?

What confuses me is that according to Faraday's Law, the electric field around the circular conductor is given by

##\nabla \times \textbf{E} = - \frac{\partial \textbf{B}}{\partial t}##

Thus for any point on the conductor the induced electric field is the same. Then going from any point along the induced electric field till reaching the same point one gets a voltage drop. For any 2 different points ##a, b## on the circular conductor I can always go from ##b## to ##a## or from ##a## to ##b## "along the induced electric field" and get voltage drops for both cases.

Could any one help to resolve the part that confuses me?