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Two long coaxical insulated solenoid's S...

Two long coaxical insulated solenoid's `S_1` and `S_2` of equal lengths are would one over the other as shown in figure. A steady current `'T'` flows through the inner solenoid `S_1` to the other end B, which is connected to the outer solenoid `S_2` through which the same current flows in opposite direction so as to come out at end A. If `n_1` and `n_2` are the number of turns per unit length, find the magnitude and direction of net magnetic field at a point (i) inside on the axis and (ii) outside the combined system.

Text Solution

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(i) At a point inside on the axis.
Magnetic field due to current I through `S_1`
`B_1=mu_0n_1i`, along `BA`, and
Magnetic field due to current i through `S_2`
`B_2=mu_0n_2i`, along AB
`:.` Net magnetic field `=B_1-B_2`
`=mu_0i(n_1-n_2)`, along BA
(ii) At a point outside the combined system, net magnetic field=Zero.
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