Question

Three charges, +2.5 micro coulomb, -4.8 micro coulomb and 6.3 micro coulomb, are located at (0.20m, .15m), (.50m, -.35m), and (-.42m,-.32m) respectively. What is the electric field at the origin?

Answer 1

To do this you need to take each charge one at a time. Use E = kq/r^2 for each to get the magnitude (you'll have to do a little pythagorean for each to get r) and the direction will be either towards or away from the origin along the line formed by the point and the origin. Frankly it's probably easier to do a tan-1 and find the angle, then do sin and cos to find the components. Sum the three x and y components for the final vector.
For example for the first
E = 9e9 * 2.5e-6 / .25^2 at an angle of tan-1(.15/.2) = 36.9o away from the origin. Find x, y components. Do same for the other two.