`AB` is a resistanceless conducting rod which forms a diameter of a conducting ring of radius `r` rotating in a uniform magnetic field `B` as shown in figure. The resistance `R_(1)` and `R_(2)` do not rotate. Then the current through the resistor `R_(1)` is

Options

A. `(B omega r^(2))/(2R_(1))`
B. `(B omega r^(2))/(2R_(2))`
C. `(B omega r^(2))/(2R_(1)R_(2))(R_(1)+R_(2))`
D. `(B omega r^(2))/(2(R_(2)+R_(2)))`

Answer

A

Explanation

The equivalent diagram is

The induced emf across the centre and any point on the circumference is
`|vec(e)| = (1)/(2)B omega l^(2) = (B omega r^(2))/(2)`
`:.` current through `R_(1) = (B omega r^(2))/(2 R_(1))`