In: Physics
when charge is accelerated through a potential difference V
let the speed be v
using Work energy theorm
q * V = 0.5 * m * v^2
v = sqrt(2 * q * V /m)
the radius of circular path , R = m * v /(q * B)
R = m * (sqrt(2 * q * V /m)) /(q * B)
the radius of path is directly proportional to the square root of potential difference
when V' = 3 V
the new radius , R' = sqrt(3) * R
so the correct option is C) sqrt(3) R