Question

The wire loop `PQRSP` formed by joining two semicircular wires of radii ` R_(1)` and `R_(2)` carries a current `I` as shown . The magnitude of the magnetic induction at the center `C` is ………..

Answer 1

The effect of current in PQ and RS for producing mangnetic field
at centre is zero.
Magnetic field due to current in semi-
circular arc `QAR=1/2[(mu_0)/2 I/(R_1)]` dir-
ected towards the reader perpendicu-
lar to the plane of paper.
Magnetic field due to current in semicircular arc `SBP=1/2[(mu_0)/2 I/(R_2)]`
directed away form the reader perpendicular to the plane of paper.
`:. Net magnetic field =1/2[(mu_0)/2 I/(R_1)]-1/2[(mu_0)/2 I/(R_2)]`
(directed towards the reader perpendicular to plane of paper).
`=(mu_0)/4[ I/(R_1)- I/(R_2)]`