The magnetic field in the cylindrical region shown in figure increases at a constant rate of 10.0 mT s − 1 . Each side of the square loop abcd and defa has a length of 2.00 cm and a resistance of 2.00

Question

The magnetic field in the cylindrical region shown in figure increases at a constant rate of $10.0 mT s^{- 1}$ . Each side of the square loop abcd and defa has a length of 2.00 cm and a resistance of $2.00Ω$ . Correctly match the current in the wire ad in four different situations as listed in List-I with the values given in List-II.

List - I	List - II
(P) The switch $S_{1}$ is closed but $S_{2}$ is open	(1) $5 \times 1 0^{- 7} A$ , d to a
(Q) $S_{1}$ is open but $S_{2}$ is closed	(2) $5 \times 1 0^{- 7} A$ , a to d
(R) both $S_{1}$ and $S_{2}$ are open	(3) $2.5 \times 1 0^{- 8} A$ , d to a
(S) both $S_{1}$ and $S_{2}$ are closed	(4) no current flows
	(5) $2.5 \times 1 0^{- 8} A$ , a to d

TestHub · Accepted Answer

Switch S 1 ​ is closed: circuit edaf is complete emf = − d t d ϕ ​ = 4 × 1 0 − 4 × 10 × 1 0 − 3 i = R emf ​ = 8 4 × 1 0 − 6 ​ = 5 × 1 0 − 7 A , a to d switch S 2 ​ is closed, S 1 ​ is open: i = 5 × 1 0 − 7 A from d to a both switches open ⇒ no current both switches closed ⇒ no current through a to d

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