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:

Step-by-step solution

The magnetic field ((B) ) at a point induced by a flowing current ((I) ) is given as, (B= ₀ I 2 r ) Where ( ₀ ) is the permeability of free space, and (r ) is the radius of the circular path. Substituting for (I ) and rearranging, ( aligned & B= ₀ ( e v 2 r ) 2 r & B= ₀ e v 4 r^2 & r^2= ₀ e v 4 B & r^2 v B & r v B aligned ) Therefore, when an electron moves in a circular orbit with a uniform speed (v ) and produces a magnetic field (B ) at the centre of the circle, the radius of the circle is proportional to ( v B