A long solenoid carrying a current produces a magnetic field B along its axis. If the current is doubled and the number of turns per cm is halved, the new value of magnetic field will be equal to

Solution

Physics sir · 3 steps

Inside a long solenoid, B depends on the product of turns per length and current, so watch that product.

1. Field inside. Deep inside a long solenoid the field is uniform. It depends only on n, the number of turns per unit length, and on the current I.

   B = μ₀ n I

2. Apply the changes. The current becomes 2I and the turns per unit length become n/2. So B' = μ₀ (n/2)(2I) = μ₀ n I.
3. So. The doubling and the halving cancel, so B' = B. The answer is (a).

The idea to keep. For a long solenoid, B = μ₀ n I with n as turns per unit length. Length and radius do not appear, so only the product nI decides the field.

Answer from the NTA final answer key. Solution by PrepWiser.