Question

A cylindrical region of radius R contains a uniform magnetic field parallel to its axis. The field is zero outside the cylinder. If the magnitude of the field is changing at the rate dB/dt, the electric field induced at a point 2R from the cylinder axis is:

a.zero
b.2R∙dB/dt
c.R∙dB/dt
d.(R/2)∙dB/dt
e.(R/4)∙dB/dt

Answer 1

The electric field induced at a point 2R from the cylinder axis is (R/4)∙dB/dt.

Step-by-step explanation:

The electric field induced at a point 2R from the cylinder axis can be determined using Faraday's law of electromagnetic induction. Faraday's law states that the induced electric field is equal to the rate of change of magnetic flux through a surface. In this case, the magnetic field is changing at a rate dB/dt, and the surface we are considering is a circle with radius 2R.

The magnetic flux through this circle is given by Ο = B * A, where B is the magnetic field and A is the area of the circle. The area of the circle is π * (2R)^2 = 4πR^2. Therefore, the magnitude of the electric field induced is given by E = -(dΟ/dt) = -(d/dt)(B * A) = -(d/dt)(B * 4πR^2) = -4πR^2 * (dB/dt).

So, the electric field induced at a point 2R from the cylinder axis is option e. (R/4)∙dB/dt.