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28. Magnetic Fields and Forces

Circular Motion of Charges in Magnetic Fields

28. Magnetic Fields and Forces

Circular Motion of Charges in Magnetic Fields

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Circular Motion of Charges in Magnetic Fields

Circular Motion of Charges in Magnetic Fields

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Anderson Video - Motion of Charge in Fields

Anderson Video - Motion of Charge in Fields

Anderson Video - Cyclotron Motion

Anderson Video - Cyclotron Motion

Path of charged particle in magnetic field | Moving charges & magnetism | Physics | Khan Academy

Path of charged particle in magnetic field | Moving charges & magnetism | Physics | Khan Academy

Khan Academy India - English

Uniform Circular Motion in a Magnetic Field (Charged Particle Trajectory, Cyclotron/Accelerator)

Uniform Circular Motion in a Magnetic Field (Charged Particle Trajectory, Cyclotron/Accelerator)

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Textbook Question

A beam of protons traveling at 1.20 km/s enters a uniform magnetic field, traveling perpendicular to the field. The beam exits the magnetic field, leaving the field in a direction perpendicular to its original direction (Fig. E27.24) . The beam travels a distance of 1.18 cm while in the field. What is the magnitude of the magnetic field?

Textbook Question

In a cyclotron, the orbital radius of protons with energy 300 keV is 16.0 cm. You are redesigning the cyclotron to be used instead for alpha particles with energy 300 keV. An alpha particle has charge q = +2e and mass m = 6.64x10^-27 kg. If the magnetic field isn't changed, what will be the orbital radius of the alpha particles?

Textbook Question

A deuteron (the nucleus of an isotope of hydrogen) has a mass of 3.34x10^-27 kg and a charge of +e. The deuteron travels in a circular path with a radius of 6.96 mm in a magnetic field with magnitude 2.50 T. (a) Find the speed of the deuteron. (b) Find the time required for it to make half a revolution. (c) Through what potential difference would the deuteron have to be accelerated to acquire this speed?

Textbook Question

Cyclotrons are widely used in nuclear medicine for producing short-lived radioactive isotopes. These cyclotrons typically accelerate H- (the hydride ion, which has one proton and two electrons) to an energy of 5 MeV to 20 MeV. This ion has a mass very close to that of a proton because the electron mass is negligible—about 1/2000 of the proton's mass. A typical magnetic field in such cyclotrons is 1.9 T. (a) What is the speed of a 5.0-MeV H-? (b) If the H- has energy 5.0 MeV and B = 1.9 T, what is the radius of this ion's circular orbit?

Textbook Question

What is the radius of a hydrogen atom whose electron moves at 7.3×10^5 m/s?

Textbook Question

(II) What strength of magnetic field is used in a cyclotron in which protons make 3.5 x 10⁷ revolutions per second?

Textbook Question

A particle of charge q moves in a circular path of radius r perpendicular to a uniform magnetic field B. Determine its linear momentum in terms of the quantities given.

Textbook Question

Suppose the Earth’s magnetic field at the equator has magnitude 0.50 x 10⁻⁴ T and a northerly direction at all points. Estimate the speed a singly ionized uranium ion ( m = 238 u, q = e) would need to circle the Earth 5.0 km above the equator. Can you ignore gravity? [Ignore relativity.]

Textbook Question

A proton and an electron have the same kinetic energy upon entering a region of constant magnetic field. What is the ratio of the radii of their circular paths?

Textbook Question

(II) For a particle of mass m and charge q moving in a circular path in a magnetic field B, (a) show that its kinetic energy is proportional to r² , the square of the radius of curvature of its path. (b) Show that its angular momentum is L=qBr² , around the center of the circle.

Textbook Question

(II) A particle of charge q moves in a circular path of radius r in a uniform magnetic field B (→ above B) . If the magnitude of the magnetic field is doubled, and the kinetic energy of the particle remains constant, what happens to the angular momentum of the particle?

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