# Physics Lesson 16.11.1 - Induced Electric Fields

Welcome to our Physics lesson on Induced Electric Fields, this is the first lesson of our suite of physics lessons covering the topic of Induced Electric Fields, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.

## Induced Electric Fields

We have seen in the previous tutorials that any change in the electric flux when a loop is placed inside a magnetic field results in the induction of a current and electromotive force in the loop. Now, let's see whether this phenomenon is somehow related to electric field. If such a relationship is proven, the true statement "an electric field generates a magnetic field around it" will have its true corresponding counter-statement "a changing magnetic field on a loop generates an electric field in it". In this way, we will have the logical relationship

E ⟹ B and B ⟹ E so E ⟺ B

To prove the above hypothesis, let's insert a copper ring of radius r inside a uniform magnetic field B as shown in the figure. The external magnetic field fills a cylindrical volume of radius R.

If we increase uniformly the strength of the external magnetic field, the magnetic flux through the ring will increase at a steady rate and as a result, a current (and emf) is induced in the ring based on the Faraday's Law. We can determine the direction of these two induced quantities (both of them are anticlockwise here) considering the Lentz Law. Thus, since the flux increases, it is like approaching the north pole of a bar magnet towards the ring in the inwards (onto the page) direction. As a result, a new magnetic field is induced in the opposite direction (out of page). As a result, we find out using the curled right hand rule that the direction of the induced current and emf is anticlockwise.

Remark! To determine the direction of the induced current, you must consider only the direction of the induced magnetic field inside the ring when applying the curled right hand rule.

Moreover, the presence of the induced current in the copper ring implies the presence of an electric field because no current can exist without an electric field around it (an electric field is required to do the necessary work for making the electrons flow around the loop). Since the electric field always has the direction of positive changes (and therefore the direction of current), we appoint an anticlockwise direction to it, just like the other two quantities discussed earlier (induced current and emf). This induced electric field is similar to that produced by static charges, as discussed in Section 14. Both fields will exert an electric force F = Q0 ∙ E on a positive test charge Q0.

From the situation described above, we reach in a very important conclusion, which represents another version of the Faraday's Law:

"A changing magnetic field in a coil induces an electric field in it."

In this way, the hypothesis provided at the beginning of this tutorial is confirmed as true. We write

E ⟹ B and B ⟹ E so E ⟺ B

The electric field induced due to the change in the magnetic flux (and field) occurs even when no copper ring is present. This means this phenomenon can occur in every medium, even in vacuum. If the copper ring is replaced with a whatever circular path of radius r, everything said above is still valid.

Due to the increase in the rate of magnet's motion described earlier, the magnetic field inside the circular path increases at a rate of ΔB/Δt. The electric field produced due to this change is tangent to the circular path; this occurs for all similar circular paths, regardless their distance from the centre of loop. Therefore, we obtain some concentric circles representing the induced electric field in various distances from the centre as shown in the figure below.

The electric field will exist as long as the magnetic flux through the loop is changing. This means when the magnetic flux is constant, no induced electric field is present around the loop. Hence, for a constant magnetic flux the circular field lines will not appear anymore in the figure.

If the magnetic flux through the circular path decreases due to any decrease of magnetic field, the electric field will reappear again but this time the field lines are in the opposite direction to before (here clockwise).

Thus, we conclude that an induced electric field is produced every time the magnetic flux (caused by a change in the magnetic field) is changing by time.

You have reached the end of Physics lesson 16.11.1 Induced Electric Fields. There are 3 lessons in this physics tutorial covering Induced Electric Fields, you can access all the lessons from this tutorial below.

## More Induced Electric Fields Lessons and Learning Resources

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16.11Induced Electric Fields
Lesson IDPhysics Lesson TitleLessonVideo
Lesson
16.11.1Induced Electric Fields
16.11.3A New Approach on Electric Potential

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