Question 1

A charged particle of mass $$m$$ and charge $$q$$ enters a region with a uniform magnetic field $$\vec{B}$$ perpendicular to its velocity $$\vec{v}. $$What is the radius $$r of $$the circular path it follows?

Accepted Answer

$$r = \frac{mv}{qB}$$

Question 2

In a mass spectrometer, ions with the same charge $$q$$ and velocity $$v$$ but different masses $$m$$ are sent through a uniform magnetic field $$B. $$Which of the following statements is correct about their trajectories?

Accepted Answer

Ions with greater mass will have a larger radius of curvature.

Question 3

A velocity selector uses perpendicular electric and magnetic fields to allow only particles with a specific velocity to pass through undeflected. What is the condition for the velocity $$v of $$these particles?

Accepted Answer

$$v = \frac{E}{B}$$

Question 4

A proton moves in a circle of radius $$r in a $$uniform magnetic field $$B$$ with speed $$v. If $$the magnetic field strength is doubled, what happens to the radius of the path?

Accepted Answer

The radius is halved.

Question 5

In a mass spectrometer, singly-ionized atoms with the same velocity $$v$$ but different masses $$m$$ are detected at different positions along a linear detector. What is the relationship between the detected position (radius $$r) $$and the mass $$m$$?

Accepted Answer

$$m \propto r$$

Question 6

A particle of charge $$q$$ and mass $$m$$ enters a region with a uniform magnetic field $$B at $$velocity $$v$$ perpendicular to the field. What is the period $$T of $$its circular motion?

Accepted Answer

$$T = \frac{2\pi m}{qB}$$

Question 7

Which of the following best explains why a deviation from a perfectly circular path in a mass spectrometer indicates a non-uniform magnetic field?

Accepted Answer

A non-uniform magnetic field causes the magnetic force to vary, changing the radius of curvature.

Question 8

A mixture of ions with the same charge and velocity passes through a mass spectrometer. If the detector shows hits at increasing distances from the entry point, what can be inferred about the mass of the ions?

Accepted Answer

The mass of the ions increases with distance from the entry point.

Question 9

A particle with charge $$q$$ and mass $$m$$ moves with velocity $$v$$ perpendicular to a magnetic field $$B. $$What is the magnitude of the magnetic force acting on the particle?

Accepted Answer

$$F = qvB$$

Question 10

In a velocity selector, if the electric field $$E is $$increased while the magnetic field $$B$$ remains constant, what happens to the velocity of the particles that pass through undeflected?

Accepted Answer

The velocity increases.

Question 11

A singly-charged ion with mass $$m$$ and velocity $$v$$ enters a mass spectrometer with a magnetic field $$B. If $$the radius of its path is $$r$$, what is the expression for its mass?

Accepted Answer

$$m = \frac{qBr}{v}$$

Question 12

Which of the following is NOT a correct application of the right-hand rule for the force on a positive charge moving in a magnetic field?

Accepted Answer

The force is in the same direction as the velocity.

Question 13

A mass spectrometer is used to analyze a mixture of isotopes. If two isotopes have the same charge but different masses, how will their paths differ in the magnetic field?

Accepted Answer

The heavier isotope will have a larger radius of curvature.

Question 14

If a particle's velocity is not perpendicular to the magnetic field, what type of path will it follow?

Accepted Answer

A helical (spiral) path.

Question 15

A particle of mass $$m$$ and charge $$q is $$moving with velocity $$v in a $$region with a uniform magnetic field $$B. If $$the velocity is doubled, what happens to the radius of the circular path?

Accepted Answer

The radius doubles.

Magnetic Fields, Forces, and Applications: Velocity Selector & Mass Spectrometer

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