Question

A charge particle after being accelerated through a potential difference ‘V’ enters in a uniform magnetic field and moves in a circle of radius r. If V is doubled, the radius of the circle will become ______.

Options

• 2r

• `sqrt 2` r

• 4r

• `r/sqrt 2`

Answer 1

A charge particle after being accelerated through a potential difference ‘V’ enters in a uniform magnetic field and moves in a circle of radius r. If V is doubled, the radius of the circle will become `bbunderline(sqrt 2 r)`.

Explanation:

When a charged particle is accelerated through a potential difference V, 

`1/2 mv^2` = qv

⇒ v = `sqrt((2 q V)/m)`

Radius in magnetic field:

r = `(m v)/(q B)`

Since v ∝ `sqrt V`,

∴ r ∝ `sqrt V`

If V is doubled,

r' = `sqrt 2 r`