Question

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 3 T, the field at the center of C would be : (Assume that the magnetic field is confined within the volume of respective solenoid).

• A. 1 T
• B. 9 T
• C. 6 T
• D. 12 T

Hint:

Treat identical solenoids in a circuit like identical resistors. The magnetic field strength will scale linearly with the current branching.

Answer 1

The Correct Option is A

Step 1: The magnetic field inside a solenoid is $B = \mu_0 n I$. Since they are identical, $B \propto I$.
Step 2: Solenoid A is in series with the parallel bank of B, C, and D. If current $I$ enters A, it splits equally into $I/3$ for B, C, and D (since they are identical).
Step 3: $B_A \propto I = 3 \text{ T}$. $B_C \propto I/3 = \frac{3 \text{ T}}{3} = 1 \text{ T}$.