A particle with unknown mass and charge moves with a constant speed v = 1.9 x 10^6 m/s as it passes undeflected through a pair of parallel plates, as shown above. The plates are separated by a distance d = 6.0 x 10^-3 m, and a constant potential difference V is maintained between them. A uniform magnetic field of magnitude B = .2 T directed into the page exists both between the plates and in a region to the right of them as shown. After the particle passes into the region to the right of the plates where only the magnetic field exists, its trajectory is circular with radius .1 m.
a. What is the sign of the charge of the particle? Justify your answer.
b. On the diagram, clearly indicate the direction of the electric field between the plates. Justify your answer.
c. Determine the magnitude of the potential difference V between th plates.
d. Determine the ratio of the charge to the mass (q/m) of the particle.
B = kI/r
F = qvBsin*
F = BIL sin*
V = IR
V = Er
F = qE
E = Blv
F = mv^2/r (centripetal force should act on the particle after its trajectory becomes circular)
The Attempt at a Solution
a. I am not sure how I would be able to determine this, honestly. Could anyone give me something to ponder about that might help me solve this?
b. Using the right hand rule, if the B is directed into the page, the force is down and current is to the left. If the force is down, then the electric field will be down as will if the charge is positive, or up if the charge is negative.
c. If I used E = V/r and E = vBL, I could say that V = vBLr, which are the 4 unknown's that I have (L being replaced by d)
d. The mass and charge could be determined by F = qvB = mv^2/r, but that would give me two unknown's. However, I was wondering, if the charge was positive or negative, could I just use the mass of a proton or electron (or even neutron) for the mass and solve for the charge from the above equation (and then finding the ratio)?
Thanks for any help at all :)