A straight conductor of mass m and carrying a current i is hinged at one end and placed in a plane perpendicular to the magnetic field of intensity B as shown in the figure. At any moment if the conductor is let 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 elementary portion of the current carrying conductor is given as
`dF = I ( dr) B sin 90 ^(@)`
`= iB dr `
The torque applied by dF about O.
`dT = rdF`
the total torque about O.
` ""_(t) = int d tau = int _(0) ^(1) r(iB) dr =(iBL^(2))/(2)`
the angular acceleration ,
`alpha = ( tau ) /( i) = ( iBL ^(2)//2) /( mL ^(2)//3)=(3i B)/(2m)`