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JEE Main 2021 (18 Mar, Shift 1) · Ampere's Law, Cylinders, Solenoid & Toroid

Ampere's Law, Cylinders, Solenoid & Toroid question from JEE Main 2021 (18 Mar, Shift 1)

Q46JEE Main 2021 · 18 MAR · SHIFT 1Difficult

Ampere's Law, Cylinders, Solenoid & Toroid

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).

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Answer: (d)

Identical solenoids: $B = \mu_0 n I \propto I$ .
A carries the full current $i$ ; B, C, D are identical and in parallel, so each carries $\frac{i}{3}$ .
$B_C = \frac{3\text{ T}}{3} = 1$ T
So the answer is (d) 1 T.

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