A conducting circular loop of area 1 mm2 is placed co-planarly with a long, straight wire at a distance of 20 cm from it. The straight wire carries as electric current which changes from 10 A to zero in 0.1 s. Find the average emf induced in the loop in 0.1 s.


Given:


Area of circular loop


Separation between wire and loop


Current through the wire



We know that magnetic field (B) due to an infinitely long wire carrying a current i at a perpendicular distance d from the wire is given by



Also,


Average induced emf in time interval Δt is given by



Where


are flux across the cross section at time intervals respectively.


Magnetic flux due to magnetic field B through cross section area A is given by



Since magnetic field due to long wire is perpendicular to the circular loop, initial magnetic flux through the loop is given by



After time interval of 0.1s current in the wire becomes zero and hence magnetic field



Average induced emf is given by




Therefore, average emf induced in the loop in time interval of 0.1s is given by 10-10V


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