Question

An electron of mass 'm' revolving around the nucleus in a circular orbit of radius 'r' has angular momentum 'L'. The magnetic field produced by the electron at the centre of the orbit is e = electric charge, µ₀ = permeability of free space ____________.

Options

• `(mu_0 "eL")/(4 pi"mr"^2)`

• `(mu_0 "eL")/(2 pi"mr"^3)`

• `(mu_0 "eL")/(2 pi"mr"^2)`

• `(mu_0 "eL")/(4 pi"mr"^3)`

Answer 1

An electron of mass 'm' revolving around the nucleus in a circular orbit of radius 'r' has angular momentum 'L'. The magnetic field produced by the electron at the centre of the orbit is e = electric charge, µ₀ = permeability of free space `(mu_0 "eL")/(4 pi"mr"^3)`.

Explanation:

L = mV r

`"B" = (mu_0 "I")/(2"r")`

`= mu_0/(2"r") xx ("eV")/(2pi"r")`

`= (mu_0 "e" ("mVr"))/(4 pi"r"^2 xx "mr")`

`= (mu_0"eL")/(4 pi"mr"^3)`