Magnetic Field Produced by a Current-Carrying Solenoid
A solenoid is a long coil of wire (with many turns or loops, as opposed to a flat loop). Because of its shape, the field inside a solenoid can be very uniform, and also very strong. The field just outside the coils is nearly zero. Figure 5.33 shows how the field looks and how its direction is given by RHR-2.
The magnetic field inside of a current-carrying solenoid is very uniform in direction and magnitude. Only near the ends does it begin to weaken and change direction. The field outside has similar complexities to flat loops and bar magnets, but the magnetic field strength inside a solenoid is simply
5.27
where is the number of loops per unit length of the solenoid with being the number of loops and the length). Note that is the field strength anywhere in the uniform region of the interior and not just at the center. Large uniform fields spread over a large volume are possible with solenoids, as Example 5.7 implies.
Example 5.7 Calculating Field Strength inside a Solenoid
What is the field inside a 2.00-m-long solenoid that has 2,000 loops and carries a 1,600-A current?
Strategy
To find the field strength inside a solenoid, we use First, we note the number of loops per unit length is
5.28
Solution
Substituting known values gives
5.29
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 1,000 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, because the superconducting state is disrupted by very large magnetic fields.
Applying the Science Practices: Charged Particle in a Magnetic Field
Visit here 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 Earth’s magnetic field.