Two charged particles with different speeds move one at a time through a region of uniform magnetic field. The particles move in the same direction and experience equal magnetic forces.
A) If particle 1 has four times the charge of particle 2, which particle has the greater speed? and explain

Particle 2 to has greater speed than particle 1

Explanation:

Magnetic force of charged particles on a magnetic field is:

with F the force, q the charge of the particle, v the velocity of the particle and B the magnetic field. Because we are interested only on the magnitude of the force (we already know directions of the particles are the same). F is:

with θ the angle between the magnetic field and the velocity vector (is the same for both particle velocities):

Because the particles experience equal magnetic forces, the right-side term should have the same value for both particles, so if one particle has 4q then the other particle should have 4v to maintain the equality. This is, particle 2 to has greater speed than particle 1, exactly 4 times its speed

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