Three point charges lie along a circle of radius r at angles of 30°, 150°, and 270° as shown in the figure below. Find a symbolic expression for the resultant electric field at the center of the circle.

Answer 1

If the charges are equal, the resultant field is zero, because the points are arranged as the corners of an equilateral triangle, and you are asking for the field at the center. Because of symmetry, the fields cancel.

Answer 2

E= −keq/r^2+keq/r^2 * cos60 +keq/r^2 * cos60