Induced Electric Field Basics

[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

 

[astrokreng]

I am happy to explain the basics of induced electric fields to you. Induced electric fields refer to the creation of an electric field in a conductor due to changes in the magnetic field around it. This change in the magnetic field can be due to various reasons such as the movement of a magnet or a changing current in a nearby wire.

To answer your first question, the formula you mentioned (E=(dB/dt)*(r/2)) is specific to a circular conductor. For a rectangular conductor, the formula is slightly different and takes into account the shape and orientation of the conductor. It is given by E=(dB/dt)*(l*w/2), where l and w are the length and width of the rectangular conductor, respectively. This formula also assumes that the conductor is placed perpendicular to the magnetic field.

In response to your second question, a varying magnetic field does indeed produce an electric field. This is one of the fundamental principles of electromagnetism, known as Faraday's Law. However, the induced electric field is only present when a conductor is placed in the region of the varying magnetic field. This is because the conductor allows for the movement of charges, which creates the induced electric field.

Lastly, if there are multiple conductors in the region of the varying magnetic field, the Principle of Superposition can be applied to find the resulting electric field at a specific point. This principle states that the total electric field at a point is the vector sum of the individual electric fields produced by each conductor. However, the shape, orientation, and position of each conductor will affect the final result.

I hope this explanation helps to clarify your doubts. If you would like to learn more about induced electric fields, I recommend checking out some reputable sources such as textbooks or online articles from trusted scientific websites.