A charged particle moving in a uniform m...

A charged particle moving in a uniform magnetic field penetrates a layer of lead and thereby loses one half of its kinetic energy. How does the time period of revolution of particle change.

Text Solution

Verified by Experts

The radius of the circular path, `r=m v//qB`. If `E_K` is the kinetic energy of the particle, then
`E_K=1/2mv^2` or `v=sqrt(2E_K//m)`
`:.` radius, `r=(msqrt(2E_K//m))/(qB)=(sqrt(2mE_K))/(qB)`,
Time period `=(2pir)/(v)=(2pisqrt(2mE_K))/(qBsqrt(2K_K//m))=(2pim)/(qB)`
It means time period of revolution is independent of K.E. This shows that if KE is halved, there is no change in time period of revolution.

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circle

parabolas

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becomes