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A particle of specific charge alpha is p...

A particle of specific charge `alpha` is projected from origin with velocity `v=v_0hati-v_0hatk` in a uniform magnetic field `B=-B_0hatk`. Find time dependence of velocity and position of the particle.

Text Solution

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Velocity of particle at time is
`v(t)=v_xhati+v_yhatj+v_zhatk`
`=v_0cos(B_0alphat)hati+v_0sin(B_0alphat)hat-v_0hatk`
`v_x` and `v_y` can be found in the similar manner as done in Example 2.
the position of the particle at time `t` would be
`r(t)=xhati+yhatj+zhatk`
Here, `z=v_zt=-v_0t`
and `x` and `y` are same as in Example 2.
Hence, `r(t)=v_0/(B_0alpha)[sin(B_0alphat)hati+1-cos(B_0alphat)hatj]-v_0thatk`
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Knowledge Check

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