A straight conductor of mas m and carrying a current I is hinged at one end and placed in a plane perpendicular to the magnetic field of intensity `vec(B)` as shown in the figure. At any moment if the conductor is set free, then the angular acceleration of the conductor will be (neglect gravity)

Options

A. `(2iB)//(3m)`
B. `(3iB)/(2m)`
C. `(iB)/(2m)`
D. `(3i)/(2mB)`

Answer

B

Explanation

The force acting on the elementry protion of the current carrying conductor is given as,
`dF = I (dr) B sin 90^(@)`
`implies dF = idr`
The torque applied by dF about `O = d tau - rdF`
`implies` The total torque about `O = tau - int dt = int r (iBdr)`
`implies tau = iB underset(0)overset(L)(int) rdr = (iBL^(2))/(2)`
the angular acceleration `alpha = (tau)/(I)`
`= alpha = ((iBL^(2))/(2))//((mL^(2))/(3)) = (3iB)/(2m)`