JEE Main & Advanced Sample Paper JEE Main Sample Paper-13

  • question_answer
    Flux \[\phi \] (in weber) in a closed circuit of resistance \[10\,\Omega \] varies with time t (in seconds) according to the equation\[\phi =6{{t}^{2}}-5t+1\] . The magnitude of the induced current in the circuit at \[t=0.25\,s\] is

    A)  0.2 A                    

    B)  0.6 A             

    C)  0.8 A                    

    D)  1.2 A

    Correct Answer: A

    Solution :

     The rate of change of flux gives the included emf. Thus, \[{{Q}_{1}}+(-{{W}_{1}})={{Q}_{2}}+(-{{W}_{2}})={{U}_{B}}-{{U}_{A}}\] \[{{F}_{net}}=\frac{{{q}^{2}}\sqrt{2}}{4\pi {{\varepsilon }_{0}}{{a}^{2}}}+\frac{{{q}^{2}}}{4\pi {{\varepsilon }_{0}}{{(\sqrt{2}a)}^{2}}}\]                 As \[{{F}_{net}}=\left( \frac{1+2\sqrt{2}}{2} \right)\,\frac{{{q}^{2}}}{4\pi {{\varepsilon }_{0}}{{a}^{2}}}\] \[l=\frac{V}{R}=\frac{9}{9}\,=1\,A\] \[R=9\,\Omega \] Induced current \[l=\frac{E}{R}=\frac{2}{10}=0.2\,A\]


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