A conducting disc of radius r rotates with a small but constant angular velocity ω about its axis. A uniform magnetic field B exists parallel to the axis of rotation. Find the motional emf between the center and the periphery of the disc.

Question

Philoid · Accepted Answer

Given:

Radius = r

Angular velocity = w

Magnetic field = B

Diagram:

Formula used:

In this case, the velocity will increase radially.

Let us consider a strip of width dx at a distance x from the centre.

Hence, induced emf of this portion will be , where B = magnetic field, dx = width of the element, x = distance of the element from the centre, w = angular velocity

Hence, integrating on both sides using proper limits, we get

=> Total motional emf (Ans)