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 anypointin the circuit is equal to the product of current flowing in the circuit and time interval. From Faraday's Und 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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