# Why is induced electric field circular?

1. Dec 9, 2015

### turaturer

Time-varying magnetic field makes electric field circular(or close loop). I am asking the reason why it is circular or close loop shape?

2. Dec 9, 2015

### cnh1995

The fields are non-conservative. They have to follow the laws of electromagnetism ( discovered by Faraday and Maxwell). In this case, electric field is induced only when there is change in magnetic flux associated with a loop (real or hypothetical).
So,∫ E⋅dl=dΦB/dt.
Since the varying flux is associated with a loop, the electric field lines are circular, i.e. they are along the loop. Everything is governed by Maxwell's mighty equations.

3. Dec 9, 2015

### Staff: Mentor

Any vector field can be decomposed into an irrotational part and a solenoidal part. Faraday discovered that the solenoidal part is equal to the time variation of the magnetic field.

4. Dec 9, 2015

### turaturer

Thank you. But I asked how time-variation of the magnetic field makes electric field rotate, not make it divergence field.

5. Dec 9, 2015

### Staff: Mentor

Yes. That is what I answered. "Faraday discovered that the solenoidal part..."

Faradays law says $\nabla \times E =\partial B/\partial t$. In words this says that the circular part of E is equal to the change of B.

Last edited: Dec 9, 2015