A metal rod of resistance `20 Omega` is fixed along a diameter of a conducting ring of radius `0.1 m` and lies on `x-y` plane. There is a magnetic field `vec(B) = (50 T)vec(k)`. The ring rotates with an angular velocity `omega = 20rad s^(-1)` about its axis. An external resistance of `10 Omega` is connected across the center of the ring and rim. The current external resistance is

Options

A. `1/2A`
B. `1/3A`
C. `1/4A`
D. 0

Answer

B

Explanation

Here, resistance of rod = `20 Omega, r=0.1 m`
B=50 T along z-axis, `omega = 20 rad s^(-1)`
Potential difference between centre of the ring and the rim is
`epsi = 1/2 B omega r^2 = 1/2 xx 50 xx 20 xx (0.1)^2= 5V`
The equivalent circuit of the arrangement is shown in figures.


`(1)/(R_P) =1/10 + 1/10 = 2/10 = 1/5 " or " R_P = 5Omega`
Current through external resistance
`I =(epsi)/(R+r ) = (5)/(10 + 5) = 1/3 A`