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Question description
Ive tried to answer the problem but Im pretty sure that everything I did was wrong.
Heres the problem.
This fun problem relates to physics. In case youre not a physics major, we urge you to follow the immortal advice of Douglas Adams: Dont Panic! You dont need to be Marie Curie to solve this one. Let M be a vector in three-space.
A constant magnetic field of value M exists at all points of three-space.
(a) Suppose M = . What is the value of the magnetic field experi- enced at the point (3, 2, ?3)? [Hint, this is not a trick question, its a warm-up]
A particle of unit mass and unit electric charge is in the field and it experiences velocity along the vector v. The field acts on the particle via the Lorentz force F = v × M. Since this force is perpendicular to v and M, by the laws of physics it does no work, and thus it can change the direction of the particle but not its
speed. If v is perpendicular to M then the particle will circle in a plane perpendicular to M. The radius of the circle is equal to |v|/|M|.1
(b) Suppose the particle is at the point (3, 2, ?3) and v = . What is the particles charge and in which direction is it going to move? [Hint, this is also meant to be a softball question.]
(c) Suppose that the particle is observed to be travelling along the circle (cos t, sin t, 0) in the x,y-plane. What is the velocity v of the particle at time t? Use Mathematica to plot in a single graph the circle and the velocity vector at some point on the circle. What magnetic field M could be acting on the particle?
(d) What sort of trajectory do you expect if the particle acquires a velocity component parallel to M? For example, what sort of trajectory do you expect if M = and v = ? A qualitative answer is accept- able here.
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