Concepts Of Physics MCQ Edition [Volume 2]PhysicsElectromagnetic Induction
A conducting disc of radius r rotates about its central axis with a small but constant angular velocity . A uniform magnetic field B is directed parallel to the rotation axis. Determine the motional emf induced between the centre and the periphery of the disc.
Options
- Ar^2 B
- B1 2 r^2 B
- C1 4 r^2 B
- D2 r^2 B
Correct answer
B. 1 2 r^2 B
Step-by-step solution
Consider a small radial element of length dx at a distance x from the centre of the disc. The linear velocity of this element is v = x . The motional emf induced across this small element is d = B v dx = B (x ) dx . The total emf induced between the centre and the periphery is obtained by integrating d from x = 0 to x = r : = ₀^ r B x dx = B [ x^2 2 ]₀^ r = 1 2 r^2 B