Question

Two long coaxial insulated solenoids, S₁ and S₂ of equal lengths are wound one over the other as shown in the figure. A steady current "I" flow thought the inner solenoid S₁ to the other end B, which is connected to the outer solenoid S₂ through which the same current "I" flows in the opposite direction so as to come out at end A. If n₁ and n₂ are the number of turns per unit length, find the magnitude and direction of the net magnetic field at a point (i) inside on the axis and (ii) outside the combined system

Answer 1

(i) The magnetic field due to a current carrying solenoid:

B=μ₀ni

where, n = number of turns per unit length
             i = current through the solenoid

Now, the magnetic field due to solenoid S₁ will be in the upward direction and the magnetic field due to S₂ will be in the downward direction (by right-hand screw rule).

B_net=BS₁−BS₂

⇒B_net=μ₀n₁I−μ₀n₂I

=μ₀I(n₁−n₂)

In the upward direction

(ii) The magnetic field is zero outside a solenoid.