AP® Physics C: E&M - Magnetic Fields -FRQs
Question
A uniform magnetic field exists in a region of space. Two experiments were done to discover the direction of the field and the following results were obtained.
A proton moving to the right with instantaneous velocity v1 experienced a force F1 directed into the page, as shown above.
A proton moving out of the page with instantaneous velocity v2 experienced a force F2 in the plane of
the page as shown above.
a. State the direction of the magnetic field and show that your choice accounts for the directions of the
forces in both experiments.
b. In which experiment did the proton describe a circular orbit? Explain your choice and determine the
radius of the circular orbit in terms of the given force and velocity for the proton and the proton mass
m.
c. Describe qualitatively the motion of the proton in the other experiment.
Answer/Explanation
Ans.
a. Experiment I demonstrated that B is in the plane of the page because F is perpendicular to both v and B
Experiment II demonstrates that B makes an angle of –60º (to the x axis) in the plane of the paper since it must
be perpendicular to F2
b. For the motion to be purely circular F must be perpendicular to v and the force is constant, while v is also
perpendicular to B, this is case II. Since F = mv2/r we have r = mv2/F
c. Since v is not perpendicular to B, the component of v parallel to v produces no force and hence no change in
motion. The perpendicular component of the velocity produces circular motion. The resulting motion is spiral
(helix) about the B vector.