A particle of charge q, mass m and kinetic energy E enters a uniform magnetic field perpendicular to its velocity and follows a circular path of radius r. Which graph in the original figure correctly represents r as a function of E?
Options

Question

A particle of charge q, mass m and kinetic energy E enters a uniform magnetic field perpendicular to its velocity and follows a circular path of radius r. Which graph in the original figure correctly represents r as a function of E?

Options

G1 Physics · Accepted Answer

For perpendicular motion in a magnetic field, qvB = mv²/r. Hence, r = mv/(|q|B). Kinetic energy is E = ½mv², so v = √(2E/m). Therefore, r = [m/(|q|B)]√(2E/m) = √(2mE)/(|q|B). Thus, r ∝ √E. The r-E graph starts at the origin and increases with decreasing slope, which is graph 4. Correct option: D.