Please, could anyone help me with this question, and the way how to do it, thank
ID: 1444990 • Letter: P
Question
Please, could anyone help me with this question, and the way how to do it, thank you for your help?
A particle with positive charge q = 1.12 10-18 C moves with a velocity v with arrow = (3i + 4j k) m/s through a region where both a uniform magnetic field and a uniform electric field exist. (a) Calculate the total force on the moving particle, taking B with arrow = (3i + 3j + k) T and E with arrow = (2i j 5k) V/m.
Fx =? N
Fy = ? N
Fz = ? N
(b) What angle does the force vector make with the positive x axis?
Explanation / Answer
q = 1.12*10^-18 C
v = 3i + 4j -k
B = 2i + 3j + k
E = 2i - j - 5k
Lorentz force F = q[E + (v x B)]
F = 1.12*10^-18 [ 2i -j -5k + (3i + 4j - k)x(2i + 3j + k)] = 1.12*10^-18 [ 2i -j -5k + 9k - 3j - 8k + 4i - 2j + 3i]
F = 1.12*10^-18 [ 9i -6j -4k] N
Fx = 10.08*10^-18 N
Fy = -6.72 * 10^-18 N
Fz = -4.48*10^-18 N
b) Angle the force vector makes with positive x axis = theta
F.i = |F|cos(theta)
cos(theta) = 1.12*10^-18 * 9 / 1.12*10^-18*11.53 = 9 / 11.53
theta = 38.68 deg