Worksheet: Motion of a Charged Particle in Combined Electric and Magnetic Fields

In this worksheet, we will practice determining the forces acting on freely moving charged particles in regions that contain both electric and magnetic fields.


An electron with a kinetic energy of 2.000 keV moves along a path that is equidistant from the surfaces of two parallel plates that are 1.00 cm apart and have a potential difference of 300 V. What is the strength of the uniform magnetic field acting parallel to the plates?

  • A1.13×10 T
  • B1.20×10 T
  • C1.50×10 T
  • D1.02×10 T
  • E1.35×10 T


An electron moving with a velocity vijk=(4.0+3.0+2.0)×10 m/s enters a region where there is a uniform electric field and a uniform magnetic field. The magnetic field is given by Bijk=(1.02.0+4.0)×10 T. If the electron travels through the region without being deflected, what is the electric field in the region?

  • A(×10ijk V/m
  • B(×10ijk V/m
  • C(×10ijk V/m
  • D(×10ijk V/m
  • E(×10ijk V/m


The magnetic field in a cyclotron is 1.25 T, and the maximum orbital radius of the circulating protons is 0.40 m.

What is the kinetic energy of the protons when they are ejected from the cyclotron?

  • A1.8×10 J
  • B1.6×10J
  • C2.5×10J
  • D2.1×10 J
  • E1.3×10 J

What is the energy of ejected protons, in MeV?

Through what potential difference would a proton have to be accelerated to acquire the kinetic energy required to eject it from the cyclotron?

What is the period of the voltage source used to accelerate the protons?

  • A6.7×10 s
  • B5.2×10 s
  • C7.3×10 s
  • D5.6×10 s
  • E6.1×10s


A charged particle moves through a velocity selector at constant velocity. In the selector, 𝐸=1.0×10 N/C and 𝐵=0.250 T. When the electric field is turned off, the charged particle travels in a circular path of radius 3.33 mm. Determine the charge-to-mass ratio of the particle.

  • A4.0×10 C/kg
  • B4.6×10/Ckg
  • C4.8×10 C/kg
  • D4.3×10 C/kg
  • E5.0×10/Ckg


Triply charged uranium-235 and uranium-238 ions have masses of 3.9×10 kg and 3.95×10 kg respectively. The ions are being separated in the 0.250 T magnetic field of a mass spectrometer, where they have a speed of 3.0×10 m/s. The ions traverse a semicircle. What is the distance between the ions in the direction perpendicular to the direction of their motion, in the plane of their motion?

  • A2.8×10 m
  • B2.1×10 m
  • C2.5×10 m
  • D1.2×10 m
  • E1.7×10 m


An electron in the cathode-ray tube of an old television moves at a speed of 5.6×10 m/s in a direction perpendicular to Earth’s magnetic field, which has a magnitude of 5.0×10 T in the region around the electron. Usually, televisions that use cathode-ray tubes are magnetically shielded so that electrons inside the tubes are not deflected by Earth’s magnetic field, but this television is not shielded. Instead, an electric field is applied perpendicular to the direction of Earth’s magnetic field and perpendicular to the direction of the electron’s velocity, which results in the electron moving in a straight line.

What is the magnitude of the applied electric field?

The applied electric field is produced between parallel plates separated by a 1.00 cm distance. What is the potential difference across the plates?


Both electrons and protons are studied in a physics laboratory that accelerates these particles linearly using an electric field in a linear accelerator and stores them after acceleration in circular rings by using magnetic fields. The maximum speed of the linearly accelerated electrons is 4.33×10 m/s.

What is the potential difference across the linear accelerator?

What is the radius of curvature of the storage ring if the ring holds protons in circular orbits after they have been accelerated by the linear accelerator in a 0.250 T field?


A particle of charge 1.6×10 C and mass 1.67×10 kg is accelerated from rest through a potential difference of 8.2 kV. The particle then enters a uniform magnetic field of strength 0.47 T, moving in a plane perpendicular to the direction of the field. What is the radius of the particle’s circular orbit in the magnetic field?


A velocity selector uses both a magnetic field of magnitude 0.051 T and an electric field of magnitude 2.2×10 V/m.

At what speed must a proton move in the selector to pass through it undeflected?

  • A5.0×10 m/s
  • B9.6×10 m/s
  • C4.3×10 m/s
  • D2.1×10 m/s
  • E6.7×10 m/s

At what speed must an alpha particle move in the selector to pass through it undeflected?

  • A4.3×10 m/s
  • B2.1×10 m/s
  • C6.7×10 m/s
  • D5.0×10 m/s
  • E9.6×10 m/s

At what speed must a singly ionized O16 atom move in the selector to pass through it undeflected?

  • A9.6×10 m/s
  • B6.7×10 m/s
  • C5.0×10 m/s
  • D2.1×10 m/s
  • E4.3×10 m/s

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