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Chapter 22 | Magnetism 1003
To find the field strength inside a solenoid, we use . First, we note the number of loops per unit length is
(22.28)
(22.29)
Solution
Substituting known values gives
Discussion
This is a large field strength that could be established over a large-diameter solenoid, such as in medical uses of magnetic resonance imaging (MRI). The very large current is an indication that the fields of this strength are not easily achieved, however. Such a large current through 1000 loops squeezed into a meter’s length would produce significant heating. Higher currents can be achieved by using superconducting wires, although this is expensive. There is an upper limit to the current, since the superconducting state is disrupted by very large magnetic fields.
Applying the Science Practices: Charged Particle in a Magnetic Field
Visit here (http://openstaxcollege.org/l/31particlemagnetic) and start the simulation applet “Particle in a Magnetic Field (2D)” in order to explore the magnetic force that acts on a charged particle in a magnetic field. Experiment with the simulation to see how it works and what parameters you can change; then construct a plan to methodically investigate how magnetic fields affect charged particles. Some questions you may want to answer as part of your experiment are:
• Are the paths of charged particles in magnetic fields always similar in two dimensions? Why or why not?
• How would the path of a neutral particle in the magnetic field compare to the path of a charged particle?
• How would the path of a positive particle differ from the path of a negative particle in a magnetic field?
• What quantities dictate the properties of the particle’s path?
• If you were attempting to measure the mass of a charged particle moving through a magnetic field, what would you need to measure about its path? Would you need to see it moving at many different velocities or through different field strengths, or would one trial be sufficient if your measurements were correct?
• Would doubling the charge change the path through the field? Predict an answer to this question, and then test your hypothesis.
• Would doubling the velocity change the path through the field? Predict an answer to this question, and then test your hypothesis.
• Would doubling the magnetic field strength change the path through the field? Predict an answer to this question, and then test your hypothesis.
• Would increasing the mass change the path? Predict an answer to this question, and then test your hypothesis.
There are interesting variations of the flat coil and solenoid. For example, the toroidal coil used to confine the reactive particles in tokamaks is much like a solenoid bent into a circle. The field inside a toroid is very strong but circular. Charged particles travel in circles, following the field lines, and collide with one another, perhaps inducing fusion. But the charged particles do not cross field lines and escape the toroid. A whole range of coil shapes are used to produce all sorts of magnetic field shapes. Adding ferromagnetic materials produces greater field strengths and can have a significant effect on the shape of the field. Ferromagnetic materials tend to trap magnetic fields (the field lines bend into the ferromagnetic material, leaving weaker fields outside it) and are used as shields for devices that are adversely affected by magnetic fields, including the Earth’s magnetic field.
PhET Explorations: Generator
Generate electricity with a bar magnet! Discover the physics behind the phenomena by exploring magnets and how you can use them to make a bulb light.
Figure 22.43 Generator (http://cnx.org/content/m55399/1.4/generator_en.jar)
