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04:33It 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?
A scientist measuring the resistivity of a new metal alloy left her ammeter in another lab, but she does have a magnetic field probe. So she creates a 6.5-m-long, 2.0-mm-diameter wire of the material, connects it to a 1.5 V battery, and measures a 3.0 mT magnetic field 1.0 mm from the surface of the wire. What is the material's resistivity?
A wire along the x-axis carries current I in the negative x-direction through the magnetic field . Find an expression for the net torque on the wire about the point x = 0.
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.
An electromagnetic rail gun uses magnetic forces to launch projectiles. FIGURE P29.76 shows a 10-cm-long, 10 g metal wire that can slide without friction along 1.0-m-long horizontal rails. The rails are connected to a 300 V source, and a 0.10 T magnetic field fills the space between the rails. Each rail has linear resistivity ⋋ = 0.10 Ω/m, which means that the resistance is ⋋ multiplied by the length of rail through which current flows. Assume that the sliding wire and the left end, where the voltage source is, have zero resistance. The wire is initially placed at x₀ = 5.0 cm then the switch is closed. What is the wire's speed as it leaves the rails?
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?
