A current loop `ABCD` is held fixed on the plane of the paper as shown in figure. The arcs `BC( radius = b) and DA ( radius = a)` of the loop are joined by two straight wires `AB and CD` at the origin `O` is 30^(@)`. Another straight thin wire with steady current `I_(1)` flowing out of the plane of the paper is kept at the origin .

The magnitude of the magnetic field (B) due to the loop `ABCD` at the origin (o) is :

Options

A. `(mu_(0)I)/(4pi)[[b-a)/(ab)]`
B. `(mu_(0)I)/(4pi) [2(b-a) + (pi)/(3) (a +b)]`
C. zero
D. `(mu_(0)I(b-a))/(24ab)`

Answer

2

Explanation

Magnetic filed due to loop `ABCD`
`= (mu_(0)I)/(4pi)((pi)/(6)) xx [(1)/(a) - (1)/(b)] = (mu_(0)I)/(24) [(b-a)/(ab)]` .