Problem 1a: Velocity Selector: Show that with the right ratio ofelectric to magnetic field strength a particle of velocity v willproceed through both fields in a straight line at constant speed(hint: you will need an equation containing v. Also: what does thestraight line at constant speed give you?). Assume that the angleof the velocity vector relative to the magnetic field vector is 90degrees.
b: Show mathematically that the charge magnitude and sign do notmatter.
c: Draw and label the electric field vector, the electric forcevector, the magnetic field vector, the velocity vector and themagnetic force vector. Hint: start with the two force vectors. Theyhave to add to zero. Then use the vector nature of the Eq = F(E)equation and the right hand rule to get the other vectors.) Assumethat the particle is negatively charged. Use into and out of thepage vector notation where necessary.
d. Explain in terms of what happens with the force vectors whenthe charge sign changes to allow a particle of either charge signpass through the velocity selector at constant velocity v. In otherwords, explain physically why the particle charge sign makes nodifference.
e. Explain in terms of what happens with the force vectors whenthe charge magnitude changes. In other words, explain physicallywhy the charge magnitude makes no difference in the velocityselector.
