Will the compass needle show deflection when the switch in the circuit shown by Fig. is closed?

No, the compass needle will not show deflection even though the switch is closed, because there is no source of electric current (Battery or cell). An electric cell or battery needs to be connected here. In the absence of electric current, there is no magnetic field produced by the wires. Hence there is no deflection.
Two identical circular loops \(P\) and \(Q\) each of radius \(r\) are lying in parallel planes such that they have common axis. The current through \(P\) and \(Q\) are \(I\) and \(4I\) respectively in clockwise direction as seen from \(O\). The net magnetic field at \(O\) is: 
Find magnetic field at midpoint O. Rings have radius $R$ and direction of current is in opposite sense. 

