A charged particle is moving in a uniform magnetic field in a circular path. Radius of circular path is `R`. When energy of particle is doubled, then new radius will be

Options

A. radius will become `r/2`
B. radius will be `rsqrt2`
C. radius will be `r/sqrt2`
D. radius will not change

Answer

C

Explanation

`1/2mv^(2)=R_K thereforem^(2)v^(2)=2mE_K and mv=sqrt(2mE_K) andr=(mv)/(qB)=sqrt(2mE_K)/(qB)therefore rpropto sqrt(E_K)therefore ` `r_(2)/r_(1)=sqrt((E_(K))/(2))/(E_(K)))=sqrt(1/2) therefore r_(2)=(r_(1))/(sqrt(2)) or (r)/(sqrt(2))`.