**Exercise 16.17 (Electric Potential at the Center of the Triangle)**

Part A = 3.4 * 10^{5} V

Part B = 2.2 * 10^{5} V

**Solutions Below:**

Part A

_{1}= 4.5 μC, q

_{2}= 3.8 μC, q

_{3}= -4.0 μC?

Express your answer using two significant figures.

The first step is to find the distance from each vertex to the center of the triangle. Since all 3 sides of the triangle are the same, we know this is an equilateral triangle and we can use the formula sqrt(3)/3 * l, where l is the length of a side. This is just geometry. There are also other ways to solve for the center, but this is the simplest, in my opinion.

So the distance to the center is:

sqrt(3)/3 * l

sqrt(3)/3 * 0.2

= 0.11547m

We also have to convert all of the μC values to C. μC is 1*10^{-6}C: 0.0000045, 0.0000038, and -0.0000040.

The formula for electric potential is given by V = kQ/d. We have to solve this formula for each vertex, but the distance to the center will be the same for all 3, since this is an equilateral triangle:

V = kQ/d

V = kQ_{1}/d + kQ_{2}/d + kQ_{3}/d

So:

V = k/d * (Q_{1} + Q_{2} + Q_{3})

V = 8.9875 * 10^{9} / 0.11547 * (0.0000045 + 0.0000038 – 0.0000040)

V = 334686

Now here’s where Mastering Physics gets dicey- two significant figures would be 330000 V, or 3.3 * 10^{5} V, but the “correct” answer to this problem is 3.4 * 10^{5} V. I don’t know if this is a rounding issue or what, but this is typical Mastering Physics behavior, as I’m sure you know.

3.3 * 10^{5} V

Part B

_{2}and q

_{3}i the figure ?

Express your answer using two significant figures.

First find the height of the triangle (this will be the distance that q_{1} is from the point of interest). Use the Pythagorean theorem. The base will be 10cm (cut the triangle in half):

0.2^{2} = 0.1^{2} + h^{2}

0.04 = 0.01 + h^{2}

h^{2} = 0.03

h = 0.1732

Now solve using the same formula as Part A. Points q_{2} and q_{3} will have distances of 0.1m, whereas q_{1} will be 0.1732m away:

V = k * (Q_{1}/d + Q_{2}/d + Q_{3}/d)

V = 8.9875 * 10^{9} * (0.0000045/0.1732 + 0.0000038/0.1 – 0.0000040/0.1)

V = 215534

Now convert to 2 significant figures:

2.2 * 10^{5} V

The calculator and explanation don’t work for me…

Unfortunately there was a problem in the calculator. It should be fixed now, although there is a rounding glitch in the problem that so far we have not been able to figure out. The glitch is a problem with Mastering Physics itself, but may not always appear.