# Three Charged Particles Injected into a Uniform Magnetic Field

See attached file for diagram.

Please solve and explain.

Three charged particles are injected into a uniform magnetic field -- all of the particles have the same speed, but their masses and charges are different. Which of the following statements are true?

1. (T/F) Particle #2 is negatively charged

2. (T/F) If they all have the same mass, then particle #2 has the greatest charge (in magnitude)

3. (T/F) Particle #3 is positively charged

4. (T/F) Particles #1 and #2 definitely must have the same sign of charge

5. (T/F) If they all have the same charge, then particle #1 has the greatest mass

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#### Solution Preview

Please refer to the attachment.

Lorentz force formula : Force experienced by a charged particle (charge q) moving in a magnetic field B with a velocity v is given by : F = q(v X B) where F is the force vector, v is the velocity vector and B is the magnetic field vector.

Magnitude of the force is given by F = qvBsinÎ¸ where Î¸ is the angle between the vectors v and B. Direction of the force vector is given by the direction rule of vector (cross) multiplication of two vector say A and B which states as follows :

A

O Î¸

B

Direction of the vector A X B is obtained by imagining a screw placed at point O perpendicular to the plane of the two vectors and rotating it in the direction from the first vector (A here) ...

#### Solution Summary

This solution helps answer question regarding particles injected in a uniform magnetic field.