A long straight current carrying wire passes normally through the centre of a circular loop if the current through the wire increases will there be an induced emf in the loop? Justify.

Hint: By the current carrying wire PQ the magnetic field is produced, will be towards the plane of the circular wire and the magnetic field is increasing. It is the right hand thumb rule that decides the direction of the magnetic field a circular loop produces. In the circular loop the direction of flow of the current in this case is represented by the curl of the fingers of the right hand and by the thumb the direction of the magnetic field is represented.

Complete step-by-step solution:
There will be no induced emf in the loop because no change is there in the magnetic flux linked with the circular loop because to the plane of the loop magnetic field lines are parallel.
\[\varphi \]= B.A
Between the field line as the angle and \[{90^ \circ }\] is the area vector, linked with the loop, we have zero flux. \[\varphi \]
\[
  \varphi = BA\cos \theta \\
  \varphi = BA\cos {90^ \circ }\varphi \\
  \varphi = 0 \\
 \]
Hence, a change in current of wire will not create any emf in the loop.

Note: By a changing magnetic field, now we also know that the direction of the electric current induced in a circular circuit is such that the magnetic field is produced by the induced current that opposes the changing magnetic field. In the conducting circular loop, the direction of the induced current is anti-clockwise.