# Which is induced first EMF or Electric field?

I am quite amazed by the reasoning given by my teacher about induced electric field and induced EMF.Well,the case was of a closed conducting loop placed in a time varying but uniform(in space) magnetic field.

He said that that EMF is induced first that's why a non conservative and non electrostatic electric field is induced which drives the free electrons in the loop.

I think that electric field is induced first which is responsible for the induction of EMF in the loop!

Please explain which is induced first?

I'm pretty sure they are the same thing, so its simultaneous.

Consider Maxwell's Equation:

$$\nabla \times \vec{E}=-\frac{\partial\vec{B}}{\partial t}$$

Our Electric field has a non-zero vector derivative if we have a time varying Magnetic field.

EMF is equal to the negative time derivative of the Magnetic flux:

$$\epsilon=-\frac{d\Phi_B}{dt}=-\frac{d}{dt}\int\vec{B}\cdot \hat{n} \ dA$$

Where $$\hat{n}$$ is the unit normal to the plane of the current loop, and $$dA$$ is differential area. Assuming space invariance of a time varying field, the time derivative can be taken into the integral and applied to the magnetic field before performing the integral.

Then we can apply Stoke's Theorem.

$$\int -\frac{\partial\vec{B}}{\partial t} \cdot \hat{n} dA=\int(\nabla \times \vec{E})\cdot \hat{n} dA=\int\vec{E}\cdot d\vec{l}=\epsilon$$

The EMF is the line integral, but the line integral is the area integral of the vector space derivative, or curl, of the Electric Field.