A) \[6\times {{10}^{-\,4}}\,\,V\]
B) \[48\,\,m\,V\]
C) \[6\times {{10}^{-\,2}}\,\,V\]
D) \[48\,\,k\,V\]
Correct Answer: B
Solution :
| B due to solenoid \[={{\mu }_{0}}ni\] |
| Flux through the coil \[=N\times B\times A\] |
| Area of coil where \[A=1.2\times {{10}^{-3}}{{m}^{2}}\] |
| N= number of turns in coil = 300 |
| Flux = \[=\phi =300\,\,\times \,\,{{\mu }_{0}}ni\,\,\times \,\,1.2\,\,\times \,\,{{10}^{-\,3}}\] |
| Current initial value = 2 Amp |
| final current \[=-\,2Amp\] |
| \[\Delta i=-\,4\,\,Amp\] |
| \[\Delta \phi =300{{\mu }_{0}}n\,\,\times \,\,1.2\times {{10}^{-\,3}}\Delta \,i\] |
| \[\Delta t=0.25\,\,sec\] |
| \[emf=-\frac{\Delta \phi }{\Delta t}\{Faraday\,\,law\}\]\[=-\,300\,\,\times \,\,{{\mu }_{0}}n\,\,\times \,\,1.2\,\,\times \,\,{{10}^{-\,3}}\frac{\Delta i}{\Delta t}\] |
| \[emf=-\,300\,\,\times \,\,4\pi \,\,\times \,\,{{10}^{-\,7}}\times \frac{2000}{0.3}\,\,\times \,\,1.2\,\,\times \,\,{{10}^{-\,3}}\frac{(-\,4)}{0.25}\]\[=1000\,\,\times \,\,4\pi \,\,\times \,\,{{10}^{-\,7}}\,\,\times \,\,2\,\,\times \,\,1.2\,\,\times \,\,4\,\,\times \,\,4\] |
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