Two infinitely long conducting wires are located at x=-R and x=R, as shown below. The wires both have negatively charged, with a linear charge density of -λ, and are parallel to the y-axis. A small charged particle with mass m and electric charge of -q, is released from rest at a small distance of a (a<<R), at point A.
a) What is the net force (magnitude and direction) on the particle, at point A? (Ignore gravity)(5pt)
b) What is the maximum electric potential energy of this particle? (5pt)
c) This particle will oscillate around the center at x=0. How long will it take the particle to come back to point A? (5pt) (Hint:You need to use what you have learned about simple harmonic motion in PHY2048 and use the approximation of
R2 − a2 ≈ R2) (This hint is only for part d, and should not be used for part a,b,c)
d) what will happen to a positively charged particle if released from resta at point A