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An electron moves in a circular orbit wi...

An electron moves in a circular orbit with a uniform speed v. It produces a magnetic field B at the centre of the circle. Prove that the radius of the circle is proportional to `sqrt(V/B)`.

Text Solution

Verified by Experts

Electric current corresponds to the revolution of electron is
`I = (eV)/(2 pi r)`
Magnetic field due to circular current at the centre
`B = mu_(0)/(4pi) *(2pii)/r = mu/(4pi) * (ev)/r^2`
`r = sqrt(prop_(0)/(4pi)*(ev)/B)r`
`r = prop sqrt(v/B)`
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