Force on a Moving Charged Particle in a Magnetic Field
Studio Physics I
Part A – Introduction
1. Consider a stream of electrons in a cathode ray tube moving through a magnetic
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field. They experience a force known as the Lorentz force: F  qv  B . Define the
variables in the equation and give the SI units for them.
2. If a magnet is held with its north pole pointed toward the top of the page as shown
at the bottom of the figure above, what is the direction of the magnetic field (as it
comes directly out of the pole)? What will be the direction of the force on an electron
moving right (remember q = –e)? Use right, left, up, down, into page, out of page.
3. If a magnet is held with its south pole pointed toward the top of the page, what is
the direction of the magnetic field? What is the direction of the Lorentz force?
4. If a magnet is held with its north pole pointed to the left as shown at the right of
the figure above, what will be the direction of the Lorentz force?
Part B – An Electron Moving in a Circle in a Magnetic Field
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5. Consider an electron with velocity v from left to right in the presence of a uniform
magnetic field B that is into the paper. The X’s in the figure below indicate this.
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Will the electron travel in a straight line with constant v ? Why or why not?
6. The force on the moving electron due to the magnetic field is perpendicular to the
direction of motion at the instant of time shown above. Does it remain perpendicular
at all later times? Why or why not?
7. Is any work done on the particle as it moves? (Hint: What is the definition of
work? What is the angle in the dot product between force and displacement?)
Rev. 2003 Bedrosian
8. If no work is done on the electron as it moves, does its speed (the magnitude of its
velocity) change or remain the same? Why or why not?
9. Is the magnitude of the force on the electron constant as it moves? If an object
moves in a plane while acted upon by a force of constant magnitude that is always
perpendicular to its velocity, how would you describe its motion in geometric terms?
Part C – Magnetic Field of the Earth (In Our Classroom)
One way to produce a magnetic field is to pass a current through a coil of wire.
For the single coil, the magnetic field at the center of the coil can be calculated from
N 0 i
the formula: B 
, where N is the number of turns of wire on the coil, i is the
2R
current in the coil in amperes, and R is the radius of the coil in meters. 0 is an
electromagnetic constant defined to be 4 x 10–7 in SI units. For the coils we are
using today, N = 15 and R = 0.075 m. The direction of the magnetic field is
perpendicular to the plane of the coil.
We will indirectly measure the magnetic field of the earth by producing a matching
magnetic field at a right angle to the earth’s field using a coil. (To be precise, we will
actually measure the horizontal component of the earth’s magnetic field as modified
by large ferromagnetic objects in the building like steel beams.)
10. Start with no current running through the coil of wire. Place the compass on the
platform at the center of the coil. Align the compass so that the north-south line is
parallel to the plane of the coil. Leave the compass in place for steps 11 and 12.
11. If the earth's magnetic field is parallel to the plane of the coil and the magnetic
field produced by the coil is perpendicular to the plane of the coil, at what angle will
the compass needle point if the earth's magnetic field is exactly equal in magnitude to
the magnetic field produced by the current carrying coil? (Hint: See figure below.)
What is this angle?
compass aligns with B total
12. Turn the current in the coil up, watch the compass needle move, and record the
value of current that you need to deflect the compass needle to the angle you found in
step 11 above. Remember, your objective is B from coil = B from the earth.
13. Use the equation to find B from the coil, and thus indirectly B from the earth. Is
your result reasonable? You should get something around 0.1 gauss or 1 x 10–5 T.
14. Check the results obtained by some teams in other parts of the room. Why might
they have gotten different answers? (Hint: Experimental errors can’t explain all of
the differences. See the comments just before step 10.)
Rev. 2003 Bedrosian