Radio astronomers detect electromagnetic radiation at 45 MHz from an interstellar gas cloud. They suspect this radiation is emitted by electrons spiraling in a magnetic field. What is the magnetic field strength inside the gas cloud?
The magnetic field strength inside the gas cloud
The given is the Radio astronomers detect electromagnetic radiation at from an interstellar gas cloud
The objective to find the magnetic field strength inside the gas cloud
The method used here is cyclotron motion to find the magnetic field
The cyclotron motion is defined as a particle travelling in a uniform circular motion perpendicular to the magnetic field at a constant speed. The magnetic field causes the circular motion to produce a circular frequency, which is given by equation in the form
Where denotes the particle's charge, the magnetic field, and the particle's mass. The frequency is determined by the magnetic field, not the particle's velocity, as indicated by equation . We rewrite equation so that is in the form
Now we plug in the electron's , , and values to get .
The earth’s magnetic dipole moment is .
a. What is the magnetic field strength on the surface of the earth at the earth’s north magnetic pole? How does this compare to the value in Table 29.1? You can assume that the current loop is deep inside the earth.
b. Astronauts discover an earth-size planet without a magnetic field. To create a magnetic field at the north pole with the same strength as earth’s, they propose running a current through a wire around the equator. What size current would be needed?
A Hall-effect probe to measure magnetic field strengths needs to be calibrated in a known magnetic field. Although it is not easy to do, magnetic fields can be precisely measured by measuring the cyclotron frequency of protons. A testing laboratory adjusts a magnetic field until the proton's cyclotron frequency is . At this field strength, the Hall voltage on the probe is when the current through the probe is . Later, when an unknown magnetic field is measured, the Hall voltage at the same current is . What is the strength of this magnetic field?
The coaxial cable shown in FIGURE P29.56 consists of a solid inner conductor of radius surrounded by a hollow, very thin outer conductor of radius . The two carry equal currents I, but in opposite directions. The current density is uniformly distributed over each conductor.
a. Find expressions for three magnetic fields: within the inner conductor, in the space between the conductors, and outside the outer conductor.
b. Draw a graph of B versus r from to if
Although the evidence is weak, there has been concern in recent years over possible health effects from the magnetic fields generated by electric transmission lines. A typical high-voltage transmission line is above the ground and carries a current at a potential of .
a. What is the magnetic field strength on the ground directly under such a transmission line?
b. What percentage is this of the earth’s magnetic field of ?
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