A) \[Q=\frac{1}{R}.\frac{\Delta \phi }{\Delta t}\]
B) \[Q=\frac{\Delta \phi }{R}\]
C) \[Q=\frac{\Delta \phi }{\Delta t}\]
D) \[Q=R.\frac{\Delta \phi }{\Delta t}\]
Correct Answer: B
Solution :
Key Idea: The charge passes through any point in the circuit is equal to the product of current flowing in the circuit and time interval. From Farada/s second law, emf induced in the circuit \[e=\frac{\Delta \phi }{\Delta t}\] If R is the resistance of the circuit, then \[i=\frac{e}{R}=\frac{\Delta \phi }{R\Delta t}\] Thus, charge passes through the circuit, \[Q=i\times \Delta t\] \[\Rightarrow \] \[Q=\frac{\Delta \phi }{R\Delta t}\times \Delta t\] \[\Rightarrow \] \[Q=\frac{\Delta \phi }{R}\] NOTE: The charge induced does not depend whether the flux change is slow or rapid. It depends only on the change in magnetic flux.
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