Question

A point charge of -1 µC is located at the origin. A second point charge of 6 µC 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.

a.) x=?

b.) y=?

Answer 1

let q1 = -1 micro C

q2 = 6 micro C

distance between the two charges, d = sqrt(1^2 + 0.5^2)

= 1.118 m

angle made by the line which joins the two charges with +x axis, theta = tan^-1(0.5/1)

= 26.6 degrees

clearly -1 micro C < 6 micro C

so, the electron must be placed close to the -1micro C.

let r is the distance from -1 micro c where the electron is placed.

use,

k*q1*e/r^2 = k*q2*e/(r + d)^2

q1/r^2 = q2/(r +d)^2

1/r^2 = 6/(r + 1.118)^2

==> r = 0.771 m

so,

a) x = -0.771*cos(26.6)

= -0.689 m

b) y = -0.771*sin(26.6)

= -0.345 m