A charged particle of mass m = 6.4X10E-8 kg, moving with constant velocity in the y-direction enters a region containing a constant magnetic field B = 3T aligned with the positive z-axis as shown. The particle enters the region at (x,y) = (0.84 m, 0) and leaves the region at (x,y) = 0, 0.84 m a time t = 694 μs after it entered the region.
1) With what speed v did the particle enter the region containing the magnetic field?
2) What is Fx, the x-component of the force on the particle at a time t1 = 231.3 μs after it entered the region containing the magnetic field.
3) What is Fy, the y-component of the force on the particle at a time t1 = 231.3 μs after it entered the region containing the magnetic field.
4) What is q, the charge of the particle? Be sure to include the correct sign.
5) If the velocity of the incident charged particle were doubled, how would B have to change (keeping all other parameters constant) to keep the trajectory of the particle the same?
2. Relevant equations
F = ma => a = (v^2)/r
F = qvB
qvB = m(v^2)/r
3. The attempt at a solution
Question 1 Solved: v = 1901.25 m/s
Question 2: Found the distance at which it traveled, by multiplying time by the velocity. And from there i used arc length divided by radius to get theta. So, θ = s/r. Then from there I used F = m*(v^2)/r * cosθ to try and solve for the x direction.
Question 3: All I did was used F = m*(v^2)/r * θ, This answer came out to be right, how ever I do not understand why it is right. So can some one please explain to me.
Question 4: I got 48.2857, how ever I do not know if this is right, and I have no way to check.
Question 5: I said increase B by a factor of 2, how ever I do not know if this is right, and again I have no way to check it.