In the following figure a current loop is shown which is made from two circular arcs of radii a and `b (a lt b)`, connected by radial wires. Calculate the magnetic field at the centre O.

Options

A. `(mu_(0) i theta)/(4 pi a b) (b - a)`, inwards
B. `(mu_(0) i theta )/(4 pi a b) (b - a) `, outwards
C. `(mu_(0)i theta)/(3 pi a b) (b - a )`, inwards
D. Zero

Answer

B

Explanation

Wires that are connected radially produce no magnetic field at the centre as these are passing through the centre when extended backwards. Only circular arcs are producing magnetic field at the centre. The inner coil produces an outward magnetic field but the outer coil produces an inward magnetic field, hence the resultant will be the difference of the two. The outward field of the inner coil will be more than that, due to the outer arc, and hence the net magnetic field will be directed outward.
`B = theta/(2 pi) [(mu_(0)i)/(2a) - (mu_(0)i)/(2b)] = (mu_(0)i theta)/(4 pi ab) ( b - a) `
Thus, option (b) is correct.