Chapter 22, Problem 1CQ

Two charged particles move at right angles to a magnetic field and deflect in opposite directions. Can one conclude that the particles have opposite charges?

To determine

The two particle perpendicular to magnetic field deflected opposite to each other have opposite charges.

Answer to Problem 1CQ

No, the two particles that is perpendicular to magnetic field deflected opposite to each other always have different charges.

Explanation of Solution

Given info: The direction of motion of particle to the magnetic field is $90°$.

Explanation:

The charged particle in a magnetic field always deflects in the direction of the magnetic force experienced by them and the direction of the magnetic force is found by the right hand rule of magnetic force.

For positive charged particle, point the fingers of your right hand in the direction of velocity, curl of your finger in the direction of magnetic field then thumb of your right points the direction of magnetic force or the direction in which positively charged particle deflects.

Now, for negative charged particle, point the fingers of your right hand in the direction of velocity, curl of your finger in the direction of magnetic field then thumb of your right points the direction of magnetic force but reverse to the direction for positive charged particles or the direction in which negatively charged particle deflects.

From the above rule, it is clear that the particle having opposite charged only deflects opposite to each other.

Conclusion:

Therefore, two particles at right angle to magnetic field deflected opposite to each other always have different charges.