BackA 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?
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 = 6.64 x 10-27 kg. If the magnetic field isn't changed, what will be the orbital radius of the alpha particles?
A deuteron (the nucleus of an isotope of hydrogen) has a mass of 3.34 x 10-27 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?
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?
The microwaves in a microwave oven are produced in a special tube called a magnetron. The electrons orbit the magnetic field at 2.4 GHz, and as they do so they emit 2.4 GHz electromagnetic waves. What is the magnetic field strength?
Particle accelerators, such as the Large Hadron Collider, use magnetic fields to steer charged particles around a ring. Consider a proton ring with 36 identical bending magnets connected by straight segments. The protons move along a 1.0-m-long circular arc as they pass through each magnet. What magnetic field strength is needed in each magnet to steer protons around the ring with a speed of 2.5 x 107 m/s? Assume that the field is uniform inside the magnet, zero outside.
Controlled fusion is a possible future energy source that would harness the same nuclear fusion reactions that power the sun. The simplest fusion reaction is ²H⁺ + ²H⁺ → ³He⁺⁺ + n + energy, in which nuclei of two deuterium atoms fuse into a nucleus while ejecting a neutron and releasing a substantial amount of energy. Deuterium is not an element but is the name given to 'heavy hydrogen,' in which the nucleus is not simply a proton but a proton and a neutron, with atomic mass 2 u. Two positive deuterium nuclei, which repel each other, can get close enough to fuse only if they have very high speeds. This can be achieved by creating a plasma of ionized deuterium gas at a temperature of 1.0 x 10⁸ K. No material substance can contain a plasma at this temperature, so the idea is to contain the plasma with magnetic fields. Consider the simplest model of using a solenoid to confine the ions to cyclotron motion around the field lines. The plasma ions have a range of speeds, and it's necessary to contain all the ions with speeds up to three times the rms speed at the plasma temperature. What magnetic field strength is needed to keep the fastest ions in 20-cm-diameter cyclotron orbits? The actual magnetic fields are considerably more complex, but your answer is a reasonable estimate of the required field strengths.
A proton moves in the uniform fields E = 2500 k V/m and B = 0.50 k T. At t = 0 s the proton is moving in a 1.0-cm-diameter circle in the xy-plane. How many revolutions will the proton have made during this time interval?
It is shown in more advanced courses that charged particles in circular orbits radiate electromagnetic waves, called cyclotron radiation. As a result, a particle undergoing cyclotron motion with speed v is actually losing kinetic energy at the rate
How long does it take (a) an electron and (b) a proton to radiate away half its energy while spiraling in a 2.0 T magnetic field?
An electron in a cathode-ray beam passes between 2.5-cm-long parallel-plate electrodes that are 5.0 mm apart. A 2.0 mT, 2.5-cm-wide magnetic field is perpendicular to the electric field between the plates. The electron passes through the electrodes without being deflected if the potential difference between the plates is 600 V. What is the electron's speed?
An electron in a cathode-ray beam passes between 2.5-cm-long parallel-plate electrodes that are 5.0 mm apart. A 2.0 mT, 2.5-cm-wide magnetic field is perpendicular to the electric field between the plates. The electron passes through the electrodes without being deflected if the potential difference between the plates is 600 V. If the potential difference between the plates is set to zero, what is the electron's radius of curvature in the magnetic field?
What is the radius of a hydrogen atom whose electron moves at 7.3×105 m/s?
What strength of magnetic field is used in a cyclotron in which protons make 3.5 x 10⁷ revolutions per second?
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.
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.]