Two long solenoids, P and Q, each have the same total number of turns and carry the same current. Solenoid P is twice as long as solenoid Q. Find the ratio of the magnetic field strengths inside them (B_P : B_Q).

Correct answer: (b) 1 : 2

Explanation

The magnetic field inside a long solenoid is B = μ₀nI, where n = N/L is the number of turns per unit length.

Both solenoids have the same N and I, but P is twice as long (L_P = 2L_Q). So P has half as many turns per unit length:

• B_P/B_Q = n_P/n_Q = (N/2L_Q) ÷ (N/L_Q) = 1/2.

So B_P : B_Q = 1 : 2. Spreading the same turns over a greater length gives a weaker field.