An electron revolves in a circular orbit of radius r with angular speed ω . The magnetic field at the centre of electron orbit is

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TestHub · Accepted Answer

Magnetic field at the centre of circular loop.

$B = \frac{μ_{0} l}{2 r} . . . (i)$

Period of revolution of electron, where $ω =$ angular velocity of electron

$T = \frac{2 π}{ω}$

where, $ω =$ angular velocity of electron.

Current produced due to movement of electron,

$I = \frac{e}{T} = \frac{e}{\frac{2 π}{ω}} = \frac{e ω}{2 π}$

On substituting the value of $I$ in Eq. (i), we get

$B = \frac{μ_{0}}{2 r} \cdot \frac{e ω}{2 π}$

$\Rightarrow B = \frac{μ_{0} e ω}{4 π r}$

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