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Four identical long solenoids A, B, C and D are interconnected as shown in the figure. If the magnetic field at the centre of A is 3 T, what is the magnetic field at the centre of C? (Assume the field of each solenoid stays confined within its own volume.)

1. 12 T
2. 6 T
3. 9 T
4. 1 T

Correct answer: 1 T

Solution

In the standard arrangement of this problem, solenoid A carries the full current I, and after A the current divides at successive junctions so that solenoid C receives only one-third of the current that A carries. Since all four solenoids are identical (same turns per unit length n), B is directly proportional to the current. With B_A = 3 T and I_C = I_A/3, the field at C is 3/3 = 1 T.

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