Question

A particle of charge 'q' and mass 'm' moves in a circular orbit of radius 'r' with angular speed `omega`. The ratio of the magnitude of its magnetic moment to that of its angular momentum is ____________.

Options

• `("q" omega"r"^2)/(2"m")`

• `("q" omega"r"^2)/2`

• `("q" omega)/(2"mr"^2)`

• `"q"/(2"m")`

Answer 1

A particle of charge 'q' and mass 'm' moves in a circular orbit of radius 'r' with angular speed `omega`. The ratio of the magnitude of its magnetic moment to that of its angular momentum is `"q"/(2"m")`.

Explanation:

`"Magnetic moment"  mu = "iA" = "qv"/(2pi"r") xx pi "r"^2`

`= "qvr"/2      because "v" = "r"omega`

Angular momentum = L = mvr

`therefore mu/"L" = "qvr"/(2 xx "mvr")`

`= "q"/(2"m")`