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Q.

A system consists of two coaxial current carrying circular loops as shown in figure. The self inductance of loop 1 is L1 and self inductance of loop 2 is L2. Magnitude of mutual inductance is M. If at any instant current flowing through loop 1 and loop 2 are i1 and i2 respectively, then total magnetic energy of the system is

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a

12L1i12+12L2i22-Mi1i2

b

12L1i12+12L2i22+Mi1i2

c

12L1i22+12L2i12-Mi1i2

d

12L1i12+12L2i22

answer is A.

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Detailed Solution

Notice that magnetic field due to left coil is towards left. Since magnetic field due to right coil is also towards left, so it increases flux associated with left coil. To oppose it, induced current due to mutual induction opposes the original current in left coil.
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A system consists of two coaxial current carrying circular loops as shown in figure. The self inductance of loop 1 is L1 and self inductance of loop 2 is L2. Magnitude of mutual inductance is M. If at any instant current flowing through loop 1 and loop 2 are i1 and i2 respectively, then total magnetic energy of the system is