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(D) According to Faraday's law of electromagnetic induction,the induced electromotive force $E$ is given by $E = -\frac{d\phi}{dt}$. Since the speed o

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$Q$ increases

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(D) According to Faraday's law of electromagnetic induction,the induced electromotive force $E$ is given by $E = -\frac{d\phi}{dt}$. Since the speed of the magnet is doubled,the rate of change of magnetic flux $\frac{d\phi}{dt}$ increases,which means $E$ increases.Since $I = \frac{E}{R}$,where $R$ is the resistance of the coil,an increase in $E$ leads to an increase in the induced current $I$.The induced charge $Q$ is given by $Q = \int I dt = \int \frac{E}{R} dt = \int \frac{1}{R} \left( -\frac{d\phi}{dt} \right) dt = -\frac{1}{R} \int d\phi = -\frac{\Delta\phi}{R}$.Since the total change in magnetic flux $\Delta\phi$ and the resistance $R$ of the coil remain unchanged,the induced charge $Q$ remains the same regardless of the speed of the magnet.Therefore,the statement '$Q$ increases' is incorrect.

As shown in the figure,a magnet is moved with a fast speed towards a coil at rest. Due to this,the induced electromotive force,induced current,and induced charge in the coil are $E$,$I$,and $Q$ respectively. If the speed of the magnet is doubled,which of the following statements is incorrect?

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