## Mastering Physics Solutions: Exercise 16.17 (Electric Potential at the Center of the Triangle)

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

Part A = 3.4 * 105 V
Part B = 2.2 * 105 V

Solutions Below:

Part A

What is the value of the electric potential at the center of the triangle if q1 = 4.5 μC, q2 = 3.8 μC, q3 = -4.0 μC?

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*10-6C: 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 = kQ1/d + kQ2/d + kQ3/d

So:

V = k/d * (Q1 + Q2 + Q3)
V = 8.9875 * 109 / 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 * 105 V, but the “correct” answer to this problem is 3.4 * 105 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 * 105 V

Part B

What is the value of the electric potential at a point midway between q2 and q3 i the figure ?

First find the height of the triangle (this will be the distance that q1 is from the point of interest). Use the Pythagorean theorem. The base will be 10cm (cut the triangle in half):

0.22 = 0.12 + h2
0.04 = 0.01 + h2
h2 = 0.03
h = 0.1732

Now solve using the same formula as Part A. Points q2 and q3 will have distances of 0.1m, whereas q1 will be 0.1732m away:

V = k * (Q1/d + Q2/d + Q3/d)
V = 8.9875 * 109 * (0.0000045/0.1732 + 0.0000038/0.1 – 0.0000040/0.1)
V = 215534

Now convert to 2 significant figures:

2.2 * 105 V

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### 2 Responses to Mastering Physics Solutions: Exercise 16.17 (Electric Potential at the Center of the Triangle)

1. P-Diddy says:

The calculator and explanation don’t work for me…

• Mastering Physics Solutions says:

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.