Will the compass needle show deflection when the switch in the circuit shown in above figure is closed?

Hint:From Biot -savart’s law we know that change of current with time produces a magnetic field around the loop and also from Lenz’s law we know that the change of magnetic field with time induce a voltage across a current loop in kept in the magnetic field.

Complete answer:
We know that Biot -savart’s law states that change of current with time produces a magnetic field around the loop. Now, here the compass is placed inside the wire twisted in between it.And there is a bulb which is connected to the wire and the key.

Now, if we switch close the key there will be no flow of charge since the bulb is a purely resistive component hence it can’t store any kind of charge. So there will be no flow of charge after switching the key. So, if no current flows through the circuit there will be a magnetic field associated with it.

Hence, there will be no deflection of the compass.

Note: The compass will only show deflection other than the deflection by the earth’s magnetic field if a local magnetic field or magnet is placed in the vicinity of the compass. From the given circuit if there was a voltage source there would be current and that current would produce a magnetic field around the wire, which at the end would deflect the compass.