Question

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 inside the cylindrical region is proportional to:

a) r
b) r²
c) 1/r
d) 1/r²

Answer 1

The magnitude of the induced electric field inside a cylindrical region with a changing magnetic field is proportional to the radial distance r from the cylinder's axis.

Step-by-step explanation:

The magnitude of the induced electric field inside the cylindrical region of radius R, where a uniform magnetic field is changing linearly with time, is directly proportional to r, the radial distance from the cylinder's axis. This is based on Faraday's law of electromagnetic induction, which states that a changing magnetic field within a closed loop induces an electromotive force (emf) proportional to the rate of change of magnetic flux through the loop. When the magnetic field is uniform and changing over time, the induced electric field in a cylindrical geometry is found to be directly proportional to the radial distance from the axis, leading to the conclusion that the magnitude of the induced electric field is proportional to r (option a).