Question

A point charge of -1 muC is located at the origin. A second point charge of 14 muC is at x = 1 m, y = 0.5 m. Find the x and y coordinates of the position at which an electron would be in equilibrium.

Answer 1

the line join the two point charge is y = 1/2 x,

the electron needs to be located at the position that E =0, that is only possible when it on the line y = 1/2 x

and only outside the line section q1q2 E =0 is possible, since q2 = 14 uC>|q1|, electron need to close q1 =-1 uC

assume is located at (xe,1/2 xe) , then we have

r1^2 = (5/4)xe^2, r2^2 = (1-xe)^2+1/4 (1-xe)^2 = 5/4 (1-xe)^2

k|q1|/r1^2 = k q2/r2^2

r2/r1 = sqrt(q2/|q1|) = 3.742

(1-xe)/(-xe) = 3.742

1-xe = -3.742xe

2.742 xe = -1

a)

xe = -0.365 m

b)

the line join the two point charge is y = 1/2 x,

y =1/2x =1/2*.365

y =-.1825 m

the location is (-0.365 m, -0.182 m)