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 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.
Test prep for ap courses
An experimentalist fires a beam of electrons, creating a visible path in the air that can be measured. The beam is fired along a direction parallel to a current-carrying wire, and the electrons travel in a circular path in response to the wire’s magnetic field. Assuming the mass and charge of the electrons is known, what quantities would you need to measure in order to deduce the current in the wire?
the radius of the circular path
the average distance between the electrons and the wire
Electrons starting from rest are accelerated through a potential difference of 240 V and fired into a region of uniform 3.5-mT magnetic field generated by a large solenoid. The electrons are initially moving in the +
x -direction upon entering the field, and the field is directed into the page. Determine (a) the radius of the circle in which the electrons will move in this uniform magnetic field and (b) the initial direction of the magnetic force the electrons feel upon entering the uniform field of the solenoid.
In terms of the direction of force, we use the left-hand rule. Pointing your thumb in the +
x -direction with the velocity and fingers of the left hand into the page reveals that the magnetic force points down toward the bottom of the page in the –
y -direction.
A wire along the
y -axis carries current in the +
y -direction. In what direction is the magnetic field at a point on the +
x -axis near the wire?
Imagine the
xy coordinate plane is the plane of the page. A wire along the
z -axis carries current in the +
z -direction (out of the page, or
). Draw a diagram of the magnetic field in the vicinity of this wire indicating the direction of the field. Also, describe how the strength of the magnetic field varies according to the distance from the
z -axis.
The strength of the magnetic field created by current in a long straight wire is given by
is the current,
is the shortest distance to the wire, and the constant
is the permeability of free space.
The direction of the magnetic field created by a long straight wire is given by right hand rule 2 (RHR-2):
Point the thumb of the right hand in the direction of current, and the fingers curl in the direction of the magnetic field loops created by it.
The magnetic field created by current following any path is the sum (or integral) of the fields due to segments along the path (magnitude and direction as for a straight wire), resulting in a general relationship between current and field known as Ampere’s law.
The magnetic field strength at the center of a circular loop is given by
is the radius of the loop. This equation becomes
for a flat coil of
loops. RHR-2 gives the direction of the field about the loop. A long coil is called a solenoid.
The magnetic field strength inside a solenoid is
where
is the number of loops per unit length of the solenoid. The field inside is very uniform in magnitude and direction.
Conceptual questions
Make a drawing and use RHR-2 to find the direction of the magnetic field of a current loop in a motor (such as in
[link] ). Then show that the direction of the torque on the loop is the same as produced by like poles repelling and unlike poles attracting.
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