Skip to main content

Electric Fields, Charge Distributions, and the GRE

Reviewing for the GRE physics subject test, I've frequently come across questions like:

Given a distribution of discrete charges, (as shown in the diagram), determine the electric field at a given point r, (also shown in the diagram).

Formula for the Electric Field from a Distribution of Charges
The distribution of charges I've seen in sample questions have, so far, involved only finite numbers of point charges, so the electric field equation can be written as a sum:


is the distance from a charge contributing to the sum to the location where the electric field is being measured, q is the value of the particular charge, and u is the unit vector pointing from the contributing charge to the field measurement point.

This can be separated into x and y components:

where theta is the angle between the particular charge and the point where the field is being measured with respect to the x axis. Using these formulas, it's just a matter of summing up the contribution of each point charge to the electric field at the location defined by the problem.

So, the standard method is to determine the x and y contribution from each charge at the location specified by the problem, and then simply sum up all the contributions. Let's try one out:


First, we'll try the example from the diagram above:
The contributions from each charge are shown in the table below:

Here's one more example with three equal charges space equally around the unit circle:

The angles used to calculate the x and y contributions of each field are also shown.

The contributions from each charge are shown in the table below:

The Trick
Both of these examples also point out a type of 'trick' question that appears in the samples. When a set of equal charges is evenly spaced around a circle surrounding the field measurement point, the total field is 0. Watch for this pattern.

Handy Stuff
GRE Physics Sample Test [pdf]
Other links to GRE sample questions


Popular posts from this blog

Cool Math Tricks: Deriving the Divergence, (Del or Nabla) into New (Cylindrical) Coordinate Systems

The following is a pretty lengthy procedure, but converting the divergence, (nabla, del) operator between coordinate systems comes up pretty often. While there are tables for converting between common coordinate systems, there seem to be fewer explanations of the procedure for deriving the conversion, so here goes!

What do we actually want?

To convert the Cartesian nabla

to the nabla for another coordinate system, say… cylindrical coordinates.

What we’ll need:

1. The Cartesian Nabla:

2. A set of equations relating the Cartesian coordinates to cylindrical coordinates:

3. A set of equations relating the Cartesian basis vectors to the basis vectors of the new coordinate system:

How to do it:

Use the chain rule for differentiation to convert the derivatives with respect to the Cartesian variables to derivatives with respect to the cylindrical variables.

The chain rule can be used to convert a differential operator in terms of one variable into a series of differential operators in terms of othe…

Lost Phone

We were incredibly lucky to have both been in university settings when our kids were born.  When No. 1 arrived, we were both still grad students.  Not long after No. 2 arrived, (about 10 days to be exact), mom-person defended her dissertation and gained the appellation prependage Dr. 

While there are lots of perks attendant to grad school, not the least of them phenomenal health insurance, that’s not the one that’s come to mind for me just now.  The one I’m most grateful for at the moment with respect to our kids was the opportunities for sheer independence.  Most days, we’d meet for lunch on the quad of whatever university we were hanging out at at the time, (physics research requires a bit of travel), to eat lunch.  During those lunches, the kids could crawl, toddle, or jog off into the distance.  There were no roads, and therefore no cars.  And, I realize now with a certain wistful bliss I had no knowledge of at the time, there were also very few people at hand that new what a baby…

Lab Book 2014_07_10 More NaI Characterization

Summary: Much more plunking around with the NaI detector and sources today.  A Pb shield was built to eliminate cosmic ray muons as well as potassium 40 radiation from the concreted building.  The spectra are much cleaner, but still don't have the count rates or distinctive peaks that are expected.
New to the experiment?  Scroll to the bottom to see background and get caught up.
Lab Book Threshold for the QVT is currently set at -1.49 volts.  Remember to divide this by 100 to get the actual threshold voltage. A new spectrum recording the lines of all three sources, Cs 137, Co 60, and Sr 90, was started at approximately 10:55. Took data for about an hour.
Started the Cs 137 only spectrum at about 11:55 AM

Here’s the no-source background from yesterday
In comparison, here’s the 3 source spectrum from this morning.

The three source spectrum shows peak structure not exhibited by the background alone. I forgot to take scope pictures of the Cs137 run. I do however, have the printout, and…