Question

An electron moves in a circular orbit with uniform speed v. It produces a magnetic field B at the centre of the circle. The radius of the circle is [µ₀ = permeability of free space, e = electronic charge]

विकल्प

• `((mu_0"ev")/(4pi"B"))^(1//2)`

• `((mu_0"eB")/(4pi"v"))`

• `((mu_0"ev")/(4pi"B"))`

• `((mu_0"ev")/("B"))^(1//2)`

Answer 1

`((mu_0"ev")/(4pi"B"))^(1//2)`

Explanation:

The magnetic field at the center of a circular orbit of a moving electron is given by

B = `mu_0/(4pi) xx "e"/"r"^3 ("v" xx "r")`

B = `mu_0/(4pi) xx ("ev" sin theta)/"r"^2`

As, in a circular path, the angle between radius vector and velocity vector is 90°.

B = `mu_0/(4pi) xx "ev"/"r"^2`

∴ r = `((mu_0"ev")/(4pi"B"))^(1//2)`