Question

A positive charge Q is distributed uniformly along the positive y-axis between y=0 and y=a. A negative point charge, -q, lies on the positive x-axis, a distance x from the origin. Calculate the x and y components of the E-field produced by the charge distribution Q at points on the positive x axis.

Answer 1

Hi Josh ... The first thing to notice about the problem is that you are being asked to find the electric field of the charge distribution Q (which is uniformly smeared along part of the y-axis), acting at a point (x,0) on the positive x-axis. The mention of the charge -q is a red herring -- information you do not need. The E-field of the charge Q depends only on the distribution of the charge Q. The role of the -q charge is to be a test charge, such as might be used if you were going to attempt to measure the E-field. But E-field is force per unit test charge. That is, F (force vector) equals (test charge) times E (the E-field vector). Because the test charge in this particular problem is negative, the force will be opposite to the direction of the E-field, and q times the E-field strength.