The figure shows a square loop PQRS with an edge length a . The resistance of the wire PQR is r and that of PSR is 2 r . The value of the magnetic field at the centre of the loop is found to be 2 μ 0 i k π a , then what is the value of k ?

Step-by-step solution

The magnetic field due to a straight current-carrying wire is B = μ 0 I 4 π d sin α + sin β B PQR = 2 × μ 0 2 i 3 4 π a 2 sin 45 ° + sin 45 ° B PSR = 2 × μ 0 i 3 4 π a 2 sin 45 ° + sin 45 ° B net = B PQR - B PSR ⇒ B net = 2 μ 0 i 3 π a ⇒ k = 3