Question

A particle of mass m and charge q describes a circular path of radius R in a magnetic field. If its mass and charge were 2 m and `q/2` respectively, the radius of its path would be ______.

Options

• `R/4`

• `R/2`

• 2 R

• 4 R

Answer 1

A particle of mass m and charge q describes a circular path of radius R in a magnetic field. If its mass and charge were 2 m and `q/2` respectively, the radius of its path would be 4 R.

Explanation:

Magnetic force = centripetal force

`qvB = (mv^2)/R`

`qB = (mv)/R ⇒ R = (mv)/(qB)`

Form = 2m and `q"'" = q/2`

`q/2B = (2mv)/(R"'")`

`R"'" = (4mv)/(qB) = 4R`