Worksheet: Motion of Charged Particles in Uniform Magnetic Fields

In this worksheet, we will practice determining the magnetic forces on charged particles in uniform magnetic fields and the motion produced by these forces.

Q1:

An electron is traveling at 5,700 m/s when it enters a 3.5 mT uniform magnetic field that is directed perpendicularly to the direction of the electron’s motion. Find the radius of the electron’s path. Use the value 1 . 6 0 × 1 0 C for the electron’s charge and the value 9 . 1 1 × 1 0 kg for the electron’s mass. Answer to two significant figures.

  • A 4 . 6 × 1 0 m
  • B 9 . 3 × 1 0 m
  • C 1 . 1 × 1 0 m
  • D 9 . 3 × 1 0 m
  • E 1 . 9 × 1 0 m

Q2:

An electron is traveling at 3,250 m/s when it enters a 1.25 T magnetic field that is directed perpendicularly to the direction of the electron’s motion. Find the displacement of the electron from the point it enters the magnetic field to the point where its velocity is at a right angle to the direction of its velocity when it entered the field. Use the value 1 . 6 0 × 1 0 C for the electron charge and the value 9 . 1 1 × 1 0 kg for the electron mass. Answer to three significant figures.

  • A 9 . 3 0 × 1 0 m
  • B 2 . 0 9 × 1 0 m
  • C 2 . 3 2 × 1 0 m
  • D 4 . 2 3 × 1 0 m
  • E 3 . 2 7 × 1 0 m

Q3:

A particle has a charge of 160 µC. The particle enters a region containing a 420 mT uniform magnetic field, moving in the 𝑥 -direction at 360 m/s and in the 𝑦 -direction at 250 m/s, as shown in the diagram.

Calculate the magnitude of the force that acts on the particle at the point where it enters the field. Answer to two significant figures.

  • A 0.029 N
  • B 13 N
  • C 1 . 2 × 1 0 N
  • D 0.29 N
  • E 0.041 N

At what counterclockwise angle from the positive 𝑥 -direction in the 𝑥 𝑦 -plane does the force act? Answer to the nearest degree.

  • A 1 1
  • B 5 5
  • C 3 4
  • D 4 4
  • E 4 6

Q4:

A particle has a charge of 325 µC. The particle enters a region containing a 245 mT uniform magnetic field, moving in the 𝑥 -direction at 125 m/s, as shown in the diagram.

Calculate the magnitude of the force that acts on the particle at the point where it enters the field.

  • A 6 . 3 7 × 1 0 N
  • B 2 . 4 4 × 1 0 N
  • C 9 . 9 5 × 1 0 N
  • D 0.166 N
  • E 9 . 9 5 × 1 0 N

Along which axis does the force act?

  • AThe 𝑦 -axis
  • BThe 𝑥 -axis
  • CThe 𝑧 -axis

Does the force act in the positive or negative axis direction?

  • APositive
  • BNegative

Q5:

A particle has a charge of 120 µC. The particle enters a region containing a 330 mT uniform magnetic field, moving in the 𝑥 -direction at 170 m/s, as shown in the diagram. The magnetic field direction is at an angle 𝜃 = 7 5 from the 𝑦 -direction in the 𝑦 𝑧 -plane. When calculating magnetic forces on the particle, answer to two significant figures.

Calculate the magnitude of the force that acts on the particle in the 𝑥 -direction at the point where it enters the field.

  • A 0.0067 N
  • B 0.065 N
  • C 0 N
  • D 0.0065 N
  • E 0.0017 N

Calculate the magnitude of the force that acts on the particle in the 𝑦 -direction at the point where it enters the field.

  • A 0.0065 N
  • B 0.0017 N
  • C 0.065 N
  • D 0.0067 N
  • E 0 N

Calculate the magnitude of the force that acts on the particle in the 𝑧 -direction at the point where it enters the field.

  • A 0 N
  • B 0.0065 N
  • C 0.065 N
  • D 0.0067 N
  • E 0.0017 N

Q6:

A particle has a charge of 310 µC. The particle enters a region containing a 620 mT uniform magnetic field, moving in the 𝑥 -direction at 250 m/s and in the 𝑧 -direction at 170 m/s, as shown in the diagram.

Calculate the magnitude of the force that acts on the particle at the point where it enters the field. Answer to two significant figures.

At what counterclockwise angle from the positive 𝑥 -direction in the 𝑥 𝑦 -plane does the force act? Answer to the nearest degree.

Q7:

A particle with zero net charge is traveling perpendicularly to a uniform magnetic field when, at an instant 𝑡 , it decays into a positively charged particle and a negatively charged particle, both with the same mass and the same magnitude of charge. Each decay product particle is accelerated by the magnetic field and so travels along a circular trajectory. The acceleration of these particles results in them emitting electromagnetic radiation, reducing their kinetic energy and the radius of the circles in which they move. At an instant 𝑡 , both particles are moving along circular paths with half the radius of the circles that described the paths that they followed at 𝑡 . What is the ratio of the energy emitted as electromagnetic radiation by the positively charged particle between 𝑡 and 𝑡 to the kinetic energy of the original particle before it decayed?

Q8:

A particle has a charge of 2 5 5 µC. The particle enters a region of a 115 mT uniform magnetic field, moving in the 𝑦 -direction at 205 m/s, as shown in the diagram.

Calculate the magnitude of the force that acts on the particle at the point where it enters the field.

  • A 2 . 9 3 × 1 0 N
  • B 5 . 2 2 × 1 0 N
  • C 0 N
  • D 6 . 0 1 × 1 0 N
  • E 1 . 3 0 × 1 0 N

Along which axis does the force act?

  • AThe 𝑧 - a x i s
  • BThe 𝑦 - a x i s
  • CThe 𝑥 - a x i s

Does the force act in the positive or negative axis direction?

  • ANegative
  • BPositive

Q9:

A particle has a charge of 140 µC. The particle enters a region containing a 250 mT uniform magnetic field moving in the 𝑥 -direction at 160 m/s, in the 𝑦 -direction at 190 m/s, and in the 𝑧 -direction at 110 m/s, as shown in the diagram.

Calculate the magnitude of the force that acts on the particle at the point where it enters the field. Answer to two significant figures.

At what counterclockwise angle from the positive 𝑥 -direction in the 𝑥 𝑦 -plane does the force act? Answer to the nearest degree.

Q10:

A charged particle follows a circular path through a 35 µT magnetic field. The particle completes 6.8 circles per second. Find the ratio of the charge of the particle to the mass of the particle.

  • A 0 . 1 9 × 1 0
  • B 1 . 8 × 1 0
  • C 1 . 2 × 1 0
  • D 2 . 2 × 1 0
  • E 0 . 6 1 × 1 0

Q11:

An electron enters the uniform magnetic field that exists between the poles of a permanent magnet just at the bottom of the region between the poles, as shown in the diagram. The electron exits the magnetic field region traveling in the opposite direction to the one in which it had entered, emerging just at the top of the region. The electron crosses the entire length of the region perpendicular to the direction of the field as it travels through it. Find the speed at which the electron enters the field. Use the value 1 . 6 × 1 0 C for the electron charge and the value 9 . 1 1 × 1 0 kg for the electron mass. Answer to two significant figures.

  • A 6 . 0 × 1 0 m/s
  • B 3 . 5 × 1 0 m/s
  • C 3 . 5 × 1 0 m/s
  • D 6 . 9 × 1 0 m/s
  • E 5 . 9 × 1 0 m/s

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