A proton moving in a uniform magnetic field with experiences force . A second proton with experiences in the same field. What is ? Give your answer as a magnitude and an angle measured from the - axis.
Magnetic field, and its direction
Depending on whether the currents run within the same or opposing directions, two parallel wires carrying electric currents repel or attract one another, in line with Ampère.
An equation describes the magnetic force:
Where is that the charge. Rearrange equation for to be within the form
The force field for the primary proton is obtained by
The force field for the second proton is
The magnitude of the magnetic flux is obtained by
The angle formed by the elements is
shows a mass spectrometer, an analytical instrument used to identify the various molecules in a sample by measuring their charge-to-mass ratio . The sample is ionized, the positive ions are accelerated (starting from rest) through a potential difference , and they then enter a region of uniform magnetic field. The field bends the ions into circular trajectories, but after just half a circle they either strike the wall or pass through a small opening to a detector. As the accelerating voltage is slowly increased, different ions reach the detector and are measured. Consider a mass spectrometer with a magnetic field and an spacing between the entrance and exit holes. To five significant figures, what accelerating potential differences are required to detect the ions and ? See Exercise for atomic masses; the mass of the missing electron is less than and is not relevant at this level of precision. Although and both have a nominal molecular mass of , they are easily distinguished by virtue of their slightly different accelerating voltages. Use the following constants:
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.
a. What is the magnetic field strength?
b. If the maximum diameter of the electron orbit before the electron hits the wall of the tube is 2.5 cm, what is the maximum electron kinetic energy?
A -m-long, -mm-diameter aluminum wire has a potential difference of between its ends. Consider an electron halfway between the center of the wire and the surface that is moving parallel to the wire at the drift speed. What is the ratio of the electric force on the electron to the magnetic force on the electron?
A proton in a cyclotron gains of kinetic energy per revolution, where is the potential between the dees. Although the energy gain comes in small pulses, the proton makes so many revolutions that it is reasonable to model the energy as increasing at the constant rate , where is the period of the cyclotron motion. This is power input because it is a rate of increase of energy.
a. Find an expression for , the radius of a proton's orbit in a cyclotron, in terms of . Assume that at .
Hint: Start by finding an expression for the proton's kinetic energy in terms of .
b. A relatively small cyclotron is in diameter, uses a magnetic field, and has a potential difference between the dees. What is the power input to a proton, in ?
c. How long does it take a proton to spiral from the center out to the edge?
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