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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(3) √v/B. Given: an electron circling at speed v and producing field B at the centre. Idea: treat the orbiting electron as a current loop and express B in terms of v and r. Period: T=(2π r)/v, so the equivalent current is I=e/T=(ev)/(2π r). Field at the centre: B=(μ₀I)/(2r)=(μ₀ev)/(4π r²). Rearranging for r: r²=(μ₀e)/(4π)·v/B. r∝√v/B. Note this is the field the electron makes, not a field it moves in — so the usual r=mv/(eB) does not apply here.

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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