A metallic rod of length 'l' is tied to a string of length 2l and made to rotate with angular speed w on a horizontal table with one end of the string fixed. If there is a vertical magnetic field 'B' in the region, the e.m.f. Induced across the ends of the rod is

Options

A. `(2 B omega l^(2))/(2)`
B. `(3 B omega l^(2))/(2)`
C. `(4 B omega l^(2))/(2)`
D. `(5 B omega l^(2))/(2)`

Answer

D

Explanation

(d) Here, induced emf.

`e=int_(2l)^(3l) (omega x)Bdx=B(omega)([(3l)^(2)-(2l)^(2)])/(2)=(5Bl^(2)omega)/(2)`.