Two single charged ions moving perpendicularly to a uniform magnetic field (B = 0.40 T) with speeds of 5000 km/s follow circular paths that differ in diameter by 5.0 cm.What is the difference in the mass of these two ions?

Question

Quizplus · Accepted Answer

The radius of circular path of an ion moving perpendicular to a uniform magnetic field is given by r = mv/qB, where m is the mass of the ion, v is its velocity, q is its charge, and B is the magnetic field. Since the ions have the same charge and move with the same speed, their radius of circular path will differ only due to their mass. Let the masses of the two ions be m1 and m2, and let their radii be r1 and r2, respectively. Then we have:

r1 - r2 = 5.0 cm = 0.050 m
m1v/qB - m2v/qB = 0.050 m
(m1 - m2)v/qB = 0.050 m
(m1 - m2) = (0.050 m)(qB/v)
(m1 - m2) = (0.050 m)(1.6 x 10^-19 C)(0.40 T)/(5000 x 10^3 m/s)
(m1 - m2) = 3.2 x 10^-28 kg

Therefore, the difference in mass of the two ions is 3.2 x 10^-28 kg, which is closest to choice C.

Two Single Charged Ions Moving Perpendicularly to a Uniform Magnetic