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Two ions having masses in the ratio 1 : ...

Two ions having masses in the ratio `1 : 1` and charges `1 : 2` are projected into uniform magnetic field perpendicular to the field with speeds in th ratio `2 : 3`. The ratio of the radius of circular paths along which the two particles move is

A

`4:3`

B

`2:3`

C

`3:1`

D

`1:4`

Text Solution

Verified by Experts

The correct Answer is:
A
`( r_1)/(r_2)=(m_1)/(m_2)xx(v_1)/(v_2)xx(q_2)/(q_1)`.
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Knowledge Check

  • Two ions having masses in the ratio 1 : 1 and charges 1:2 are projected into a uniform magnetic field at right angles to it with speeds in the ratio 2:3 . The ratio of the radii of circular paths along which the two particles move is

    A
    `4:3`
    B
    `2:3`
    C
    `3:1`
    D
    `1:4`

  • 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 :

    A
    `4:3`
    B
    `2:3`
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    `3:2`
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    `3:4`

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    C
    `1:1:2`
    D
    `1:2:1`

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