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# Special Geometries for Electrostatics for AP Physics B & C (page 2)

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By McGraw-Hill Professional
Updated on Feb 12, 2011

### Part 1—Electric field

Electric field is a vector quantity. So we'll first find the electric field at point "P" due to charge "A," then we'll find the electric field due to charge "B," and then we'll add these two vector quantities. One note before we get started: to find r, the distance between points "P" and "A" or between "P" and "B," we'll have to use the Pythagorean theorem. We won't show you our work for that calculation, but you should if you were solving this on the AP exam.

Note that we didn't plug in any negative signs! Rather, we calculated the magnitude of the electric field produced by each charge, and showed the direction on the diagram.

Now, to find the net electric field at point P, we must add the electric field vectors. This is made considerably simpler by the recognition that the y-components of the electric fields cancel … both of these vectors are pointed at the same angle, and both have the same magnitude. So, let's find just the x-component of one of the electric field vectors:

Some quick trigonometry will find cos θ … since cos θ is defined as , inspection of the diagram shows that . So, the horizontal electric field Ex = (510 m) … this gives 140 N/C.

And now finally, there are TWO of these horizontal electric fields adding together to the left —one due to charge "A" and one due to charge "B". The total electric field at point P, then, is

280 N/C, to the left.

### Part 2—Force

The work that we put into Part 1 makes this part easy. Once we have an electric field, it doesn't matter what caused the E field—just use the basic equation F = qE to solve for the force on the electron, where q is the charge of the electron. So,

F = (1.6 × 10–19 C) 280 N/C = 4.5 × 10–17 N.

The direction of this force must be OPPOSITE the E field because the electron carries a negative charge; so, to the right.

### Part 3—Potential

The nice thing about electric potential is that it is a scalar quantity, so we don't have to concern ourselves with vector components and other such headaches.

The potential at point "P" is just the sum of these two quantities. V = zero!

Notice that when finding the electric potential due to point charges, you must include negative signs … negative potentials can cancel out positive potentials, as in this example.

Practice problems for these concepts can be found at:

Electrostatics Practice Problems for AP Physics B & C

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