The path of a charged particle in a uniform magnetic field depends on the angle `theta` between velocity vector and magnetic field, When `theta is 0^(@) or 180^(@), F_(m) = 0` hence path of a charged particle will be linear.
When `theta = 90^(@)`, the magnetic force is perpendicular to velocity at every instant. Hence path is a circle of radius `r = (mv)/(qB)`.
The time period for circular path will be `T = (2pim)/(qB)`
When `theta` is other than `0^(@), 180^(@) and 90^(@)`, velocity can be resolved into two components, one along `vec(B)` and perpendicular to B.
`v_(|/|)=cos theta`
`v_(^)= v sin theta`
The `v_(_|_)` component gives circular path and `v_(|/|)` givestraingt line path. The resultant path is a helical path. The radius of helical path
`r=(mv sin theta)/(qB)`
ich of helix is defined as `P=v_(|/|)T`
`P=(2 i mv cos theta)`
`p=(2 pi mv cos theta)/(qB)`
Two ions having masses in the ratio 1:1 and charges 1:2 are projected from same point into a uniform magnetic field with speed in the ratio 2:3 perpendicular to field. The ratio of radii of circle along which the two particles move is :

Options

A. `4:3`
B. `2:3`
C. `3:2`
D. `3:4`

Answer

A

Explanation

`R prop (mv)/(q)`
So, `R_(1):R_(2)=(m_1)/(m_2) xx (V_1)/(V_2) xx (q_2)/(q_1) = 1/2 xx 2/3 xx 2/1 = 4/3`
`(R_1)/(R_2)=4/3`
So, choice (a) is correct.