Two wire loop PQRSP formed by joining two semicircular wires of radii `R_(1) and R_(2)` carries a current i as shown in the figure given below. What is the magnetic field induction at the centre O in cases (A) and (B) ?

Explanation

(a) As the point O is along the length of the straight wires, so the field at O due to them will be zero and hence magnetic field is only due to semicircular portions
`therefore |vecB|=(mu_(0))/(4pi)[(pii)/(R_(2))ox+(pii)/(R_(1))odot]`
or, `|vecB|=(mu_(0))/(4pi)pii[(1)/(R_(2))-(1)/(R_(1))]` out of the page
(b) `|vecB|=(mu_(0))/(4pi)ipi[(1)/(R_(1))+(1)/(R_(2))]` into the page