| A ring of N turns with radius a and resistance R is pulled into region of magnetic field B at an angle of \[45{}^\circ \] with the horizontal as shown below. |
 |
| Charge passes through coil in time duration in which coil is completely immersed in field will be |
A) \[\frac{\pi {{a}^{2}}NB}{R}\]
B) \[\frac{\pi {{a}^{2}}NB}{\sqrt{2}R}\]
C) \[\frac{\sqrt{2}\pi {{a}^{2}}NB}{R}\]
D) \[\frac{2\pi {{a}^{2}}NB}{R}\]
Correct Answer: A
Solution :
| Current induced in coil. |
| \[i=\frac{E}{R}=\frac{1}{R}\left( \frac{d{{\phi }_{B}}}{dt} \right)\] |
| \[\Rightarrow \]\[\frac{dq}{dt}=\frac{1}{R}\frac{d{{\phi }_{B}}}{dt}\] |
| \[\Rightarrow \]\[\Delta Q=\frac{1}{R}\times \Delta {{\phi }_{B}}=\frac{\pi {{a}^{2}}NB}{R}\] |
| Total charge passing through coil is independent of time. Also, \[\frac{d\phi }{dt}\]can be determined only when velocity is given. |
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