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Q.21

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
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Short Answer

21. Scientists studying an anomalous magnetic field find that it is inducing a circular electric field in a plane perpendicular to the magnetic field. The electric field strength from the center of the circle is . At what rate is the magnetic field changing?

The rate at which the magnetic field is changing is

See the step by step solution

Step by Step Solution

Step 1. Given infomation

Radius of circle

Electric field strength

Step 2. Explanation

The induced electric field in a region where the radius of circle is less than radius of circular region the charge is confined is given by

Here is the rate of changing magnetic field, is the radius of the solenoid.

Therefore, the Rate of changing of magnetic field is given by

The rate of changing of magnetic field is given by

Substituting the values of radius , electric field strength (E) in above equation, the rate of change of magnetic field is calculated as

The values of rate of electric field strength and radius given in the question are used to calculate the changing magnetic field using the formula

The rate at which the magnetic field is changing is

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