Question

A point charge of -2.5 µC is located at the origin. A second point charge of 8 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.

1. x=

2. y=

Answer 1

Electric field due to a point charge is given by Coulomb's law as: where r is the relative position vector of the point where field is required from the point charge.

Let the coordinates where the electron is in equilibrium be (x,y). The field due the 2 charges at that point must be 0 for the electron to be in equilibrium.

....1

As there are only 2 points, the field due to them would be zero on the straight line joining them at a point not in between the 2 charges, which is given by:

Substituting this in equation 1 gives,

as the position is a point not in between the 2 charges

The correct coordinates at which the electron would be in equilibrium is