Question

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 centre and the periphery of the disc.

Answer 1

Motional EMF is Product of Length, Speed and Field

Explanation:

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 center.

Hence, induced emf of this portion will be,

dE = Blv = $Bdx \times x$ where B = magnetic field,

dx = width of the element,

x = distance of the element from the center, w = angular velocity

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

$\int_{0}^{E}dE = \int_{0}^{r}Bxwdx$

Total motional emf E = $\frac {Bwr^2}{2}$