How Does Shape Affect the Calculation of Induced Electric Fields?

[arjunarul]

I've just seen induced electric field concepts. Could anyone provide a link, which explains it?

I had some rather stupid doubts regarding it:

1.If a circular conductor is placed in a varying magnetic field, then to find the induced electric field, we take the center of the conductor as origin and get E=(dB/dt)*(r/2) at a distance r from the centre. What if the conductor is not circular, but a rectangle?

2.There is a varying magnetic field. Does it as such produce an electric field, or is the induced electric field produced only when a conductor is placed in the region?

3.What if we have more than one conductor (circular) in the region of varying magnetic field, and we want to find the electric field at some point? Do we apply Principle of Superposition?

Thanks.

 

[Bob S]

1.If a circular conductor is placed in a varying magnetic field, then to find the induced electric field, we take the center of the conductor as origin and get E=(dB/dt)*(r/2) at a distance r from the centre. What if the conductor is not circular, but a rectangle?.

This is true everywhere in the conductor. For either a rectangular or circular conductor (which includes both copper conductors and steel transformer laminations), you need to integrate over the volume of the conductor. Eddy currents vary linearly with the frequency and the square of the width of the conductor. Power loss (watts) varies as the square of the eddy currents.

2.There is a varying magnetic field. Does it as such produce an electric field, or is the induced electric field produced only when a conductor is placed in the region?.

In microwave fields (like in a microwave oven), there are both magnetic and electric fields, even when there is no conductor in the field..

3.What if we have more than one conductor (circular) in the region of varying magnetic field, and we want to find the electric field at some point? Do we apply Principle of Superposition?.

Superposition works. If you have a transformer coil with many turns with a stray ac magnetic field, there are electric fields and eddy currents induced in every conductor.
Bob S