# 19.1 Electric potential energy: potential difference  (Page 8/13)

 Page 8 / 13

What is the internal energy of a system consisting of two point charges, one 2.0 µC, and the other −3.0 µC, placed 1.2 m away from each other?

1. −3.8×10 -2 J
2. −4.5×10 -2 J
3. 4.5×10 -2 J
4. 3.8×10 -2 J

(b)

A system of three point charges has a 1.00 µC charge at the origin, a −2.00 µC charge at x =30 cm, and a 3.00 µC charge at x =70 cm. What is the total stored potential energy of this configuration?

A system has 2.00 µC charges at (50 cm, 0) and (−50 cm, 0) and a −1.00 µC charge at (0, 70 cm). As the y -coordinate of the −1.00 µC charge increases, the potential energy ___. As the y -coordinate of the −1.00 µC charge decreases, the potential energy ___.

1. increases, increases
2. increases, decreases
3. decreases, increases
4. decreases, decreases

(b)

A system of three point charges has a 1.00 µC charge at the origin, a −2.00 µC charge at x =30 cm, and a 3.00 µC charge at x =70 cm. What happens to the total potential energy of this system if the −2.00 µC charge and the 3.00 µC charge trade places?

Take a square configuration of point charges, two positive and two negative, all of the same magnitude, with like charges sharing diagonals. What will happen to the internal energy of this system if one of the negative charges becomes a positive charge of the same magnitude?

1. increase
2. decrease
3. no change
4. not enough information

(a)

Take a square configuration of point charges, two positive and two negative, all of the same magnitude, with like charges sharing diagonals. What will happen to the internal energy of this system if the sides of the square decrease in length?

A system has 2.00 µC charges at (50 cm, 0) and (−50 cm, 0) and a −1.00 µC charge at (0, 70 cm), with a velocity in the – y -direction. When the −1.00 µC charge is at (0, 0) the potential energy is at a ___ and the kinetic energy is ___.

1. maximum, maximum
2. maximum, minimum
3. minimum, maximum
4. minimum, minimum

(c)

What is the velocity of an electron that goes through a 10 V potential after initially being at rest?

## Section summary

• Electric potential is potential energy per unit charge.
• The potential difference between points A and B, ${V}_{B}–{V}_{A}$ , defined to be the change in potential energy of a charge $q$ moved from A to B, is equal to the change in potential energy divided by the charge, Potential difference is commonly called voltage, represented by the symbol $\text{Δ}V$ .
$\Delta V=\frac{\text{ΔPE}}{q}\phantom{\rule{0.25em}{0ex}}\text{and ΔPE =}\phantom{\rule{0.25em}{0ex}}q\Delta V\text{.}$
• An electron volt is the energy given to a fundamental charge accelerated through a potential difference of 1 V. In equation form,
$\begin{array}{lll}\text{1 eV}& =& \left(1.60×{\text{10}}^{\text{–19}}\phantom{\rule{0.25em}{0ex}}\text{C}\right)\left(1 V\right)=\left(1.60×{\text{10}}^{\text{–19}}\phantom{\rule{0.25em}{0ex}}\text{C}\right)\left(1 J/C\right)\\ & =& 1.60×{\text{10}}^{\text{–19}}\phantom{\rule{0.25em}{0ex}}\text{J.}\end{array}$
• Mechanical energy is the sum of the kinetic energy and potential energy of a system, that is, $\text{KE}+\text{PE}.$ This sum is a constant.

## Conceptual questions

Voltage is the common word for potential difference. Which term is more descriptive, voltage or potential difference?

If the voltage between two points is zero, can a test charge be moved between them with zero net work being done? Can this necessarily be done without exerting a force? Explain.

What is the relationship between voltage and energy? More precisely, what is the relationship between potential difference and electric potential energy?

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