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A charged particle moving in a uniform m...

A charged particle moving in a uniform magnetic field penetrates a layer of lead and there by loses one-half of its kinetic energy. How does the radius of curvature of its path change?

A

The radius increases to `r sqrt(2)`

B

The radius reduces to `r//sqrt(2)`

C

The radius remains the same

D

The radius becomes `r//2`

Text Solution

Verified by Experts

The correct Answer is:
B
`E_2 =(E_1)/(2), r_1=r,r_2 =?`
`E=(q^2 B^2 r^2)/(2m)`
`therefore E prop r^2`
`therefore r prop sqrt( E)`
`(r_2)/(r_1)=sqrt((E_2)/(E_1))`
`therefore r_2=sqrt((E_1)/(2E_1))r_1 =(r_1)/(sqrt(2))= (r ) /(sqrt(2))`.
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