Two particles of charge q1 and q2, respectively, move in the same direction in a magnetic field and experience the same magnetic force (direction and magnitude). If the speed of particle 1 is seven times faster than that of particle 2, determine the ratio |q1|/|q2| of the magnitudes of the charges.

|q1| / |q2| = 1/7

Explanation:

We are told that both particles are in the same magnetic field, B.

The charge of the first particle is q1

The charge of the second particle is q2

Let the speed of particle 1 be v1.

Let the speed of particle 2 be v2.

The magnetic force acting on particle 1 due to the magnetic field, B, is:

F1 = |q1| * v1 * B

The magnetic force acting on particle 2 due to the magnetic field, B, is:

F2 = |q2| * v2 * B

We are told that both particles experience the same magnetic force. This means that F1 = F2

Therefore:

|q1| * v1 * B = |q2| * v2 * B

=> |q1| * v1 = |q2| * v2

|q1| / |q2| = v2/v1

We are told that the speed of particle 1 is seven times that of particle 2. Hence:

v1 = 7 * v2

Hence:

|q1| / |q2| = v2 / (7 * v2)

|q1| / |q2| = 1/7