Four identical long solenoids A, B, C and D are connected to each other as shown in the figure. If the magnetic field at the center of A is 3T, the field at the center of C would be : (Assume that the magnetic field is confined with in the volume of respective solenoid).

Solution

Physics sir · 3 steps

Field inside a solenoid follows its current, so just find what fraction of i reaches C.

1. Field in a solenoid. Inside a long solenoid B = μ₀ n i. The four solenoids are identical, so n is the same for all, and B depends only on the current through each one.
2. Split the current. All of i passes through A. It then divides among B, C and D, which are in parallel. Identical solenoids have equal resistance, so each branch gets i/3.

   B_C/B_A = (μ₀ n (i/3))/(μ₀ n i) = 1/3

3. So. B_C = 1/3 × 3 T = 1 T, which is option (d).

The idea to keep. For identical solenoids, compare fields through currents alone: B ∝ i. Find how the current splits in the circuit and the fields scale the same way.

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