Length of a very long bar magnet is kept along the axis of a circular loop of radius r in such a manner that North Pole of magnet lies at the centre of circular loop. Magnitude of magnetic field due to magnet at any point on the circumference of loop is B. Current i flows through the loop. Magnetic force acting on circular loop is

Options

A. `2pi i rB` along the plane of loop
B. `2pi irB` along the axis of loop
C. `2i rB` along the axis of loop
D. Zero

Answer

B

Explanation

Bar magnet is given to be very long and hence effect of South Pole can be neglected for the field at the site of loop. Direction of magnetic field for the loop can be assumed to be radially outwards from the bar magnet centre on the plane of loop. If we select a segment of length dl on the circumference of wire then direction of current element idl is taken along the current and hence along the tangent to the loop. Field is radial and current element is tangential and hence direction of magnetic force according to d `vecF = id vecl xx vecB` will be parallel to the axis of loop. Direction of this force is same for all the segments on circumference of loop and moreover angle between `idl` and B is `90^@` for all the points. Hence net force acting on the loop is parallel to the axis of loop and its magnitude can be written as follows:
` F = int idl B sin 90^@`
` rArr F = iB intdl`
` rArr F = iB int dl`
` rArr F = iB(2pi r)`
`rArr F = 2pi r B , ` along the axis of loop .