Question

A cylindrical region of radius R = 3.0 cm contains a uniform magnetic field parallel to its axis. If the electric field induced at a point R/2 from the cylinder axis is 4.5 x 10-/ the magnitude of the magnetic field must be changing at the rate of:

a) 0
b) 0.30 T/s
c) 0.60 T/s
d) 1.2 T/s
e) 2.4 T/s

Answer 1

The rate of change of the magnetic field, denoted by dB/dt, is calculated by applying Faraday's law of electromagnetic induction, using the formula E = (dB/dt) * (r/2), where E is the electric field induced and r is the radial distance from the cylinder axis.

Step-by-step explanation:

The question asks about the rate at which the magnitude of a magnetic field within a cylindrical region is changing, given that an electric field is induced at a certain point. This is related to Faraday's law of electromagnetic induction, which suggests that a changing magnetic field induces an electric field. To answer the student's question, we use the formula derived from Faraday's law for the induced electric field in a region with a changing magnetic field: E = (dB/dt) * (r/2), where E is the induced electric field, dB/dt is the rate of change of the magnetic field, and r is the distance from the cylinder axis. We know E = 4.5 x 10^-3 V/m and r/2 = R/4 = 3.0 cm / 4 = 0.0075 m. Plugging in the values, we can solve for dB/dt.