A cylindrical region of radius R contains a uniform magnetic field, parallel to its axis, with magnitude that is changing linearly with time.If r is the radial distance from the cylinder axis, the magnitude of the induced electric field outside the cylinder is proportional to: A)R B)r C)r² D)1/r E)1/r²

Question

Quizplus · Accepted Answer

The induced electric field outside a cylindrical region with a changing magnetic field is given by Faraday's law of electromagnetic induction. According to this law, the induced electric field in a loop surrounding the cylinder (outside it) is proportional to the rate of change of the magnetic flux through the loop. Since the magnetic field is uniform and changing linearly with time, the magnetic flux change is proportional to the area of the loop, which is constant for a given radius. However, the induced electric field's magnitude is inversely proportional to the distance from the axis (r) because the circumference of the loop, which determines the path along which the electric field acts, increases with r. Therefore, the electric field strength decreases as 1/r to conserve the total induced electromotive force around the loop.

A Cylindrical Region of Radius R Contains a Uniform Magnetic