|Class 12 Physics Electromagnetic Induction||Self and Mutual Inductance|
Self and Mutual Inductance
Problem:- Two coils have mutual inductance of 1.5 H. If the current in the primary circuit is raised to 5A in 1 millisecond after closing the circuit, what is the emf induced in the secondary?
Ii=0 A, If=5A, dt =1ms =10-3sec
e2 =-M (dIi/dt)
=1.5 x ((If-Ii)/dt)
=1.5 x ((5-0)/10-3)
Problem:- Two concentric circular coils, one of small radius r1 and the other of large radius r2, such that r1<< r2, are placed co-axially with centres coinciding. Obtain the mutual inductance of the
Let a current I2 flow through the outer circular coil. The field at the centre of the coil is
B2 = μ0I2 / 2r2. Since the other co-axially placed coil has a very small radius, B2 may be considered constant over its cross-sectional area. Hence,
Φ1 = πr12 B2
=I2 (μ0 π r12)/ (2r2)
Thus, M12 = (μ0 π r12)/ (2r2)
Using equation M12=M21= (μ0 π r12)/ (2r2)
Note that we calculated M12 from an approximate value of Φ1, assuming the magnetic field B2 to be uniform over the area π r12. However, we can accept this value because r1 << r2.