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(A) The current $I$ produced by an electron moving in a circular orbit of radius $R$ with speed $v$ is given by $I = \frac{e}{T}$,where $T$ is the tim

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$\sqrt{\frac{v}{B}}$

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(A) The current $I$ produced by an electron moving in a circular orbit of radius $R$ with speed $v$ is given by $I = \frac{e}{T}$,where $T$ is the time period.Since $T = \frac{2\pi R}{v}$,we have $I = \frac{ev}{2\pi R}$.The magnetic field $B$ at the centre of the circular loop is $B = \frac{\mu_0 I}{2R}$.Substituting the value of $I$,we get $B = \frac{\mu_0}{2R} \left( \frac{ev}{2\pi R} \right) = \frac{\mu_0 ev}{4\pi R^2}$.Rearranging for $R^2$,we get $R^2 = \frac{\mu_0 ev}{4\pi B}$.Therefore,$R \propto \sqrt{\frac{v}{B}}$.

An electron moves in a circular orbit with a uniform speed $v$. It produces a magnetic field $B$ at the centre of the circle. The radius of the circle is proportional to

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