Answer to Question #86677 in Electricity and Magnetism for Chandan

Question

An electron and a proton, having the same kinetic energy, enter a region of uniform magnetic field moving perpendicular to the field. Calculate the ratio of the radii of their circular paths in the field.

Answer 1

p = 1.6x10^-19 C - charge of proton

e = -1.6x10-19 C - charge of electron

m_e = 9.1x10^-31 kg

m_p = 1.6x10^-27 kg

E_p=E_e

B = induction of magnetic field

Then force of Lorentz - F_L=evB or for proton F_L=pvB. Kinetic energy - E = mv² / 2

mv² / R_p = pvB, for electron mv² / R_e = evB

$\frac{R_p}{R_e} = \sqrt{\frac{m_e}{m_p}} \frac{p}{e} = 0.02384$