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?
A)2.6 × 10−28 kg
B)6.4 × 10−28 kg
C)3.2 × 10−28 kg
D)5.1 × 10−28 kg
E)1.1 × 10−28 kg

Question

Quizplus · Accepted Answer

We can use the equation for the radius of a circular motion in a magnetic field:
r = mv/qB

where:
r = radius of the circular path
m = mass of the ion
v = velocity of the ion
q = charge of the ion
B = magnetic field strength

Since both ions have the same charge and are moving at the same speed, the radius of their circular path will be inversely proportional to their mass. Therefore, we can set up the following equation:

m1/m2 = r2/r1

where:
m1 = mass of ion 1
m2 = mass of ion 2
r1 = radius of the circular path of ion 1
r2 = radius of the circular path of ion 2

Substituting the values given in the problem, we get:

m1/m2 = (r1 + 0.025)/(r1 - 0.025)

Simplifying the equation and solving for m1 - m2, we get:

m1 - m2 = 3.2 × 10^-28 kg

Therefore, the answer is choice C.

Two Single Charged Ions Moving Perpendicularly to a Uniform Magnetic