The circular wire loop in the x-y-plane of the diagram has a radius a = 0.1 m, i

Question

The circular wire loop in the x-y-plane of the diagram has a radius a = 0.1 m, is uniformly charged and carries a charge Q = +2 Times 10^-12 C Find the electrostatic potential at the point O = (0, 0, 0) due to the ring. Find the electrostatic potential due to the ring at the point A on the z=axis where z = 0.1 m. An electron (m = 9.11 Times 10^-31 kg, q = 1.6 Times 10^-19 C) moving upward along the z-axis passes through the center of the ring with the velocity v_0 = 2 Times 10^5/s. Calculate the velocity VA of the electron when it is at the point A. What is the acceleration's at point O? show your reasoning.

Explanation / Answer

a) Electrostatic potential at z = 0 m = kQ/r = 0.1796 V
b) At z = 0.1, V = kQ/(sqroot(z^2 + r^2)) = 0.12699 V
c) KE at A = Initial KE + Change in PE
0.5*m*(2*10^5)^2 = 0.5*mv^2 - (0.1796 - 0.12699)*q
v = 136162.4756 m/s
d) At o, acc of particle = 0 as net force is 0

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