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11. ⇒ (MHT CET 2021 20th September Morning Shift )

An electron (e) moves in circular orbit of radius 'r' with uniform speed 'V'. It produces magnetic field 'B' at the centre of circle. The magnetic field B is $(μ_{0} =$ permeability of free space)

A. $\frac{μ_{0} e}{4 π} (\frac{V}{r^{2}})$

B. $\frac{μ_{0} e}{4 π} {Vr}^{2}$

C. $\frac{μ_{0} e}{4 π} (\frac{V}{r})$

D. $\frac{μ_{0} e}{4 π} Vr$

Correct Option is (A)

Magnetic field at the centre of a circular coil is given by

$B = \frac{μ_{0} I}{2 r}$

In this case the current $I = \frac{e}{T}$ where T is the period of revolution

$\begin{aligned} T & = \frac{2 π r}{v} \\ ∴ I & = \frac{eV}{2 π r} ∴ B = \frac{μ_{0} eV}{4 π r^{2}} \end{aligned}$

⇒Magnetic Field due to Electric Current