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.

I'm not looking for an answer, more of a very detailed explanation. I had this question on an exam and cant seem to reproduce what the answer is. So whoever answers, if you could be as specific as possible it would be greatly appreciated.

Answer 1

Here is a diagram representing the problem

Answer 2

For a really detailed explanation, have a look on Youtube at the MIT 8.02 lectures on Electricity and Magnetism by Walter Lewin. There are some 30 lectures in all and they are all absolutely first rate. Walter Lewin of MIT is probably the best physics Professor out there.

Answer 3

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.

Does that make sense?

Answer 4

As different parts of the rod cause different field, you have to integrate through the rod in order to get the answer. Every infinitesimally short piece dy of the rod will have a charge dq and every of those charges will cause a field dE.

Answer 5

Thanks for the help guys. Its actually the integration part that I can't seem to get right. I should have been more specific. Also, I'll check out the lectures quantum.

Answer 6

OK, good. There are a couple of approaches to the integrals. Perhaps you have Sears and Zemansky, 12th edition, available to you. Exampl;e 21.11 on page 731 has a very similar problem, and suggests "an integral table is helpful"; In fact, in the back of the book, Appendix B, they give you the two indefinite integrals needed: integral of (1/(a^2+x^2)) ^ (3/2) power, and integral of (x/(a^2+x^2))^(3/2) power, which are what you want with change of y for x, and (constant x in your problem) for a.

But let's say the table of integrals is not available. Another textbook, "Electric and Magnetic Fields" by D.H. Tomboulian, has the problem of field due to a positive charge spread uniformly along a straight line, worked out on pp 11-12. He evaluates at a general point, not just perpendicular to end of the line as in your problem. His method for dealing with the integrals is to make a substitution x = a*tan(theta). Ending up with integration of cos(theta) and sin(theta), easy to evaluate, then substitute back and simpllify.

The Schaum's outline "Electromagnetics", 2nd edn, by Joseph Edminster, also has lots of E-field problems in chapter 2.

Finally, about resources, I've looked at the MIT course, and it is ok, but not quite up to the level I suspect you are working at. You might instead wish to take a look at the Open Yale course, by Prof Shankar, Physics 201, which is a bit more "real physics" in my opinion. ie, training for real physicists. I'm only partway into it, at lecture #7, but really enjoying it. URL is oyc.yale.edu then choose Physics, then Shankar P201.

Best wishes!