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(B) The opposing magnetic force on the loop is given by $F = B I a$,where $I$ is the induced current.Since $I = \frac{E}{R}$,where $E = B a v$ is the

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(B) The opposing magnetic force on the loop is given by $F = B I a$,where $I$ is the induced current.Since $I = \frac{E}{R}$,where $E = B a v$ is the induced emf,we have $I = \frac{B a v}{R}$.Thus,the opposing force is $F = \frac{B^2 a^2 v}{R}$.Using Newton's second law,$m \frac{dv}{dt} = -\frac{B^2 a^2 v}{R}$.Since $v = \frac{dx}{dt}$,we can write $m v \frac{dv}{dx} = -\frac{B^2 a^2 v}{R}$,which simplifies to $\frac{dv}{dx} = -\frac{B^2 a^2}{m R}$.This shows that while the loop is entering or leaving the magnetic field region,its speed decreases linearly with distance $x$.When the loop is entirely inside the magnetic field,the net magnetic flux through it is constant,so no emf is induced,and the speed remains constant.Therefore,the speed $v$ decreases,stays constant,and then decreases again,which is represented by graph $B$.

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