Question

A circular metal plate of radius R is rotating with a uniform angular velocity ω with its plane perpendicular to a uniform magnetic field B. Then the emf developed between the centre and the rim of the plate is
(a) πωBR²
(b) ωBR2(c) πωBR² / 2(d) ωBR²/ 2​

Answer 1

Correct Answer : option D: ωBR²/ 2

Explanation :

At a distance t, the velocity is  

u= φωˆ r

where φ is the angle in the x–y plane

The induced voltage is

v=∫ (uxB).dl

=∫(φωˆ r

)ˆ Bz rˆ dr

 z is along r. Hence,

V= ωB∫rdr

=ωBr²/2