An electron moves in a Bohr orbit. The magnet | vedclass

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(D) The magnetic field $B$ at the centre of a circular current loop is given by $B = \frac{\mu_0 I}{2r}$,where $I$ is the current and $r$ is the radiu

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$n^{-5}$

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(D) The magnetic field $B$ at the centre of a circular current loop is given by $B = \frac{\mu_0 I}{2r}$,where $I$ is the current and $r$ is the radius of the orbit.For an electron revolving in an orbit,the current $I = \frac{e}{T} = \frac{ev}{2\pi r}$,where $v$ is the velocity and $T$ is the time period.Substituting $I$ into the magnetic field formula: $B = \frac{\mu_0 ev}{4\pi r^2}$.According to Bohr's model,the radius $r \propto n^2$ and the velocity $v \propto n^{-1}$.Substituting these proportionalities: $B \propto \frac{v}{r^2} \propto \frac{n^{-1}}{(n^2)^2} = \frac{n^{-1}}{n^4} = n^{-5}$.Therefore,the magnetic field at the centre is proportional to $n^{-5}$.

An electron moves in a Bohr orbit. The magnetic field at the centre is proportional to

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