Two coaxial circular loops of radii 0.5m and 5 × 10 2 m are separated by a distance 0.5m and carry currents 2 A and 1 A respectively. Calculate the mutual inductance. What is the force between the loops?
Text Solution
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Sol. The coil 2 can be considered to be very small as compared to 1 ; so it can be considered on the axis of coil 1. Magnetic field due to coil 1 at a distance x on its axis is given by
B 1 = 
Flux linked with coil 2 due to magnetic field of coil 1,
φ 2 = B 1 ( 
) = 
So the mutual inductance
M = 
= 
= 
M ≅ 3.48 × 10 –9 H
U = – 
. 
= M 2 B 1
The potential energy of a coil in a magnetic field is Where M 2 is magnetic moment of coil 2 and B 1 magnetic field on it.
The force between two loops
F = – 
= 
[ 
] 
= – 
= 
F = – 2.09 × 10 –8 N
The minus sign shows that the force is attractive.
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