KVPY Sample Paper KVPY Stream-SX Model Paper-21

  • question_answer
    A solenoid has 2000 turns wound over a length of 0.3m, The area of its cross- section is \[1.2\text{ }\times \text{ 1}{{0}^{-3}}\text{ }{{m}^{2}}.\] Around its central portion a coil of 300 turns is wound. If an initial current of 2 amp in the solenoid is reversed in 0.25 sec., the emf induced in the coil is equal to -

    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  \[=-\,2Amp\]
    \[\Delta i=-\,4\,\,Amp\]
    \[\Delta \phi =300{{\mu }_{0}}n\,\,\times \,\,1.2\times {{10}^{-\,3}}\Delta \,i\]
    \[\Delta t=0.25\,\,sec\]
    \[emf=-\frac{\Delta \phi }{\Delta t}\{Faraday\,\,law\}\]\[=-\,300\,\,\times \,\,{{\mu }_{0}}n\,\,\times \,\,1.2\,\,\times \,\,{{10}^{-\,3}}\frac{\Delta i}{\Delta t}\]
    \[emf=-\,300\,\,\times \,\,4\pi \,\,\times \,\,{{10}^{-\,7}}\times \frac{2000}{0.3}\,\,\times \,\,1.2\,\,\times \,\,{{10}^{-\,3}}\frac{(-\,4)}{0.25}\]\[=1000\,\,\times \,\,4\pi \,\,\times \,\,{{10}^{-\,7}}\,\,\times \,\,2\,\,\times \,\,1.2\,\,\times \,\,4\,\,\times \,\,4\]

You need to login to perform this action.
You will be redirected in 3 sec spinner