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 9.11×10 kg for the electron mass value and 1.60×10 C for the electron charge value.

  • A1.30×10 Hz
  • B7.69×10 Hz
  • C5.09×10 Hz
  • D9.12×10 Hz
  • E2.62×10 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 I
  • BDirection II

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?

  • A𝐹
  • B𝐹
  • C𝐹
  • D𝐹

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

  • A𝐹
  • B𝐹
  • C𝐹
  • D𝐹

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.

  • A9.7×10 m/s
  • B4.2×10 m/s
  • C79×10 m/s
  • D9.2×10 m/s
  • E8.9×10 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=1.28m and the detector is located at a distance 𝑑=2𝑟 from the point where ions leave the region between the parallel plates. The ions have a charge of 3.20×10 C and a mass of 5.27×10 kg. Find the potential difference across the charged plates. Answer to three significant figures.

Q6:

Ions are emitted from a source into a region between parallel, oppositely charged plates 10.0 cm apart. The parallel plates are within a uniform magnetic field directed out of the plane of the diagram shown. The potential difference between the plates is 245 V and the magnetic field strength is 12.5 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 and the detector is located at a distance 𝑑=2𝑟 from the point where ions leave the region between the parallel plates. The ions have a charge of 3.20×10 C and a mass of 2.17×10 kg. Find the distance 𝑑. Answer to three significant figures.

Q7:

A positively charged particle moves through a region that contains two charged plates 30 cm 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 particle moves through the region along a straight path that is parallel to the negatively charged plate. The particle’s speed along its path is 240 m/s.

What is the strength of the magnetic field? Answer to two significant figures.

If the magnetic field strength is changed to 500 mT, what speed would the particle need to have to pass through the region undeflected?

Q8:

Ions are emitted from a source into a region between parallel, oppositely charged plates 7.50 cm apart. The parallel plates are within a uniform magnetic field directed out of the plane of the diagram shown. The potential difference between the plates is 895 V. 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=752mm and the detector is located at a distance 𝑑=2𝑟 from the point where ions leave the region between the parallel plates. The ions have a charge of 3.20×10 C and a mass of 4.39×10 kg. Find the strength of the magnetic field. Answer to three significant figures.

Q9:

A conducting strip of silver with a thickness of 𝑑=1.8mm is in a uniform magnetic field. A current of 1.4 A is maintained through the strip, perpendicular to the magnetic field direction, as shown in the diagram. The sides of the strip perpendicular to the current and the magnetic field are charged and have the potentials 𝑉 and 𝑉. The difference Δ𝑉 between 𝑉 and 𝑉 is 0.062 µV. Find the strength of the magnetic field. Use 1.6×10 C for the electron charge value and 5.8×10 m−3 for the conduction electron density of silver.

Q10:

A conducting metal strip with thickness 𝑑=2.2mm is in a uniform magnetic field with a strength of 712 mT. An 892 mA current is maintained through the strip, perpendicular to the magnetic field direction, as shown in the diagram. The sides of the strip perpendicular to the current and the magnetic field are charged and have the potentials 𝑉 and 𝑉. The difference Δ𝑉 between 𝑉 and 𝑉 is 0.092 µV. Find the conduction electron density of the metal from which the strip is made. Use 1.6×10 C for the electron charge value. Answer to two significant figures.

  • A2.0×10 m−3
  • B6.2×10 m−3
  • C2.0×10 m−3
  • D4.0×10 m−3
  • E4.0×10 m−3

Q11:

Ions of two isotopes of an element are emitted from a source into a region between parallel oppositely charged plates with a potential difference across them. The parallel plates are within a uniform magnetic field directed out of the plane of the diagram shown. 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. For one isotope, the curved path describes a semicircle of radius 𝑟=12.5cm and the detector is located at a distance 𝑑=2𝑟 from the point where ions leave the region between the parallel plates. The increase in the distance Δ𝑑 of the position of the detector when it is set to detect the other isotope is 3.64 cm. Find the ratio of the mass of the heavier isotope of the element to that of the lighter isotope. Answer to three significant figures. Assume that ions are always singly ionized.

Q12:

A conducting strip of silver with a thickness of 𝑑=459μm is in a uniform magnetic field with a strength of 876 mT. A current is maintained through the strip, perpendicular to the magnetic field direction, as shown in the diagram. The sides of the strip perpendicular to the current and the magnetic field are charged and have the potentials 𝑉 and 𝑉. The difference Δ𝑉 between 𝑉 and 𝑉 is 0.18 µV. Find the current through the strip. Use 1.6×10 C for the electron charge value and 5.8×10 m−3 for the conduction electron density of silver. Answer to two significant figures.

  • A0.44 A
  • B0.15 A
  • C5.6 A
  • D0.88 A
  • E1.8 A

Q13:

A positively charged particle moves through a region that contains two charged plates 26 mm apart that create a uniform electric field. An 800 mT uniform magnetic field that has a direction perpendicular to the electric field exists between the plates, as shown in the diagram. The particle moves through the region along a straight path that is parallel to the negatively charged plate. The particle’s speed along its path is 350 m/s. Find the potential difference across the plates. Answer to two significant figures.

  • A4.2 V
  • B11 V
  • C7.3 V
  • D6.2 V
  • E2.9 V

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