A circular loop of radius a, carrying a current I, is placed in a tow dimensional magnetic field. The centre of the loop coincides with the centre of the filed The strenght of the magnetic field at the pariphery of the loop is B. find the magnetic force on the wire.

Options

A. 0
B. `2 pi IRB`, outward
C. `pi IRB` , outward
D. `2 pi IRB`, inward

Answer

b

Explanation

If we select the current element` (Ivec(dl))` anywhere on the wire loop, then the magnetic field is perpendicular to it because the current element is along the tangent (according to the direction of current) and the magnetic field is stiven to be radial. Direction of ` I d vec l xx vec B` is outward for all the segments on the ring. Hence we can directly integrate to get the net force.
`d vec F = I d vecl xx vec B rArr d F = I dl B sin 90^(@) = i dl B`
`F = int dF = I underset("loop") int dlB = I (2 pi R) B`
Hence, option (b) is correct .