Worksheet: Motion of Charged Particles in Combined Uniform Magnetic and Electric Fields

In this worksheet, we will practice analyzing the motion of charged particles in perpendicularly directed uniform electric and magnetic fields.

Q1:

An electron is released into the center of a cyclotron that has a 2.75 T magnetic field. Find the frequency of the cyclotron’s oscillating electric field. Use 9 . 1 1 × 1 0 kg for the electron mass value and 1 . 6 0 × 1 0 C for the electron charge value.

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

Q2:

An electron is released into the center of a cyclotron. At the instant that the electron is introduced, the right-hand dee of the cyclotron is negatively charged. The electron is eventually ejected from the cyclotron from the point 𝑃 , as shown in the diagram. In which of the directions does the ejected electron move?

  • ADirection II
  • BDirection I

Q3:

An electron is at the center of a cyclotron at an instant when the dees of the cyclotron are charged, as shown in the diagram.

Which of the forces shown in the diagram is due to the cyclotron’s electric field?

  • A 𝐹
  • B 𝐹
  • C 𝐹
  • D 𝐹

Which of the forces shown in the diagram is due to the cyclotron’s magnetic field?

  • A 𝐹
  • B 𝐹
  • C 𝐹
  • D 𝐹

Q4:

A positively charged particle moves through a region that contains two charged plates 2.5 mm apart that create a uniform electric field. A uniform magnetic field that has a direction perpendicular to the electric field exists between the plates, as shown in the diagram. The strength of the magnetic field is 275 mT. The particle moves through the region along a straight path that is parallel to the negatively charged plate and at a distance of 1.25 mm from it. Find the particle’s speed along its path. Answer to two significant figures.

  • A 8 . 9 × 1 0 m/s
  • B 9 . 2 × 1 0 m/s
  • C 9 . 7 × 1 0 m/s
  • D 4 . 2 × 1 0 m/s
  • E 7 9 × 1 0 m/s

Q5:

Ions are emitted from a source into a region between parallel, oppositely charged plates 5.00 cm apart. The parallel plates are within a uniform magnetic field directed out of the plane of the diagram shown. The magnetic field strength is 136 mT. Ions traveling parallel to the plates at speed 𝑣 exit the region between the plates and then follow a curved path that terminates at a detector. The curved path describes a semicircle of radius 𝑟 = 1 . 2 8 m and the detector is located at a distance 𝑑 = 2 𝑟 from the point where ions leave the region between the parallel plates. The ions have a charge of 3 . 2 0 × 1 0 C and a mass of 5 . 2 7 × 1 0 kg. Find the potential difference across the charged plates. Answer to three significant figures.

  • A 650 V
  • B 791 V
  • C 984 V
  • D 560 V
  • E 719 V

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