JEE Main & Advanced Physics Electro Magnetic Induction Question Bank Graphical Questions

  • question_answer
    A flexible wire bent in the form of a circle is placed in a uniform magnetic field perpendicular to the plane of the coil. The radius of the coil changes as shown in figure. The graph of induced emf in the coil is represented by

    A)                               

    B)                        

    C)                               

    D)                                

    Correct Answer: B

    Solution :

                       \[\varphi =BA\]\[=B\times \pi {{r}^{2}}\]                    \[\therefore \varphi \propto {{r}^{2}}\Rightarrow \varphi =k{{r}^{2}}\]               (k = constant)                    \[\therefore e=\frac{d\varphi }{dt}=k.2r\frac{dr}{dt}\]                    From 0 ? 1, r is constant, \\[\frac{dr}{dt}=0\] hence, e = 0                    From 1 ? 2, \[r=\alpha t,\]\\[\frac{dr}{dt}=\alpha \] hence \[e\propto r\] Þ \[e\propto t\]            From 2 ? 3, again r is constant, \\[\frac{dr}{dt}=0\]hence e = 0


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