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 outside the cylinder is proportional to:

a) r
b) r²
c) 1/r
d) 1/r²

Answer 1

The magnitude of the induced electric field outside the cylindrical region is proportional to 1/r.

Step-by-step explanation:

The magnitude of the induced electric field outside the cylindrical region is proportional to 1/r.

This can be understood by Faraday's law of electromagnetic induction, which states that a changing magnetic field induces an electric field. In this case, the magnetic field is changing linearly with time, which results in an induced electric field.

The formula for the magnitude of the induced electric field outside the cylinder is given by:
E = -d(Br)/dt, where Br is the magnetic field at a radial distance r from the axis.

Since the magnetic field is changing linearly, the derivative of the magnetic field with respect to time is a constant. Therefore, the magnitude of the induced electric field is inversely proportional to the radial distance r, or 1/r.