An electric charge moving in a constant magnetic field tends to exhibit circular

Question

An electric charge moving in a constant magnetic field tends to exhibit circular motion, since the magnetic force always acts perpendicularly to the charge’s velocity.

a) Set the magnetic force on a charge equal to a centripetal force and solve for the radius of the circle r.

b) How would the size of a charge’s orbit change if you increased the strength of the magnetic field? Would its orbit get smaller, larger, or stay the same?

c) If a charge slowed down, how would its orbit change? Would its orbit get smaller, larger, or stay the same?

d) How would the orbit of a positive charge due to a magnetic force differ from that of a negative charge? Explain.

The formula you found in part a) is the basis for mass spectrometers. These devices are used to identify what types of atoms make up unknown samples of material. Lets say you introduced a sample of table salt (NaCl) into a mass spectrometer. When ionized the salt turns into a positive Na+ and a negative Cl-.

e) How would the motion of these two ions differ when passing through a constant magnetic field? Use the variables in your formula from part a) to justify your answer.

Explanation / Answer

a) Centripetal force = magnetic force

m*v^2/R = q*v*B

radius of the orbit is R = (m*v)/(q*B)

b) if strength of field is increased then orbit's size is also increases

answer is larger

c) if a charge is slowed down,then orbit gets smaller

d) if the orbit is turning down for positive charge ,then for a negative charge it turns up

e) motion of the two ions are opposite direction

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