A ring of mass 'm' and radius 'r' carrying current `i_(0)` is lying in the X-Y plane with centre at origin. A uniform magnetic field of strength `B=B_(0) (2hat(i)-3hatj+5hatk)T` is applied in the region. If the ring rotates about the axid initial magnetic energy stored in the ring will be. (In joules)

Options

A. `-pi^(2)i_(0)B_(0)`
B. `-5pir^(2)i_(0)B_(0)`
C. `-3pir^(2)i_(0)B_(0)`
D. `-2pir^(2)i_(0)B_(0)`

Answer

B

Explanation

`vec(M)=pir^(2)i_(0)hat(k)`
`vec(B)=B_(0)(2hat(i)-3hat(j)+5hat(k))`
`U=-vec(M).vec(B)`
`U=-5pi^(2)i_(0)B_(0)`