Part C: A point charge q3 = -5.00 μC moves from point a to point b. How much work is done on q3 by the electric forces exerted by q1 and q2? Express your answer with the appropriate units.Wab=__ ## Part A**Question:**What is the electric potential at point $ a $ due to $ q_1 $ and $ q_2 $?**Answer:**\[ V_a = 0 \, \text{V} \]### Explanation:**Correct****IDENTIFY:** The potential at any point is the scalar sum of the potentials due to individual charges.**SET UP:** \[ V = kq/r \]\[ W_{ab} = q(V_a - V_b) \]**EXECUTE:**\[ r_{a1} = r_{a2} = \frac{1}{2} \sqrt{(0.0100 \, \text{m})^2 + (0.0100 \, \text{m})^2} = 0.0071 \, \text{m} \]\[ V_a = k\left(\frac{q_1}{r_{a1}} + \frac{q_2}{r_{a2}}\right) = 0 \, \text{V} \]---## Part B**Question:**What is the electric potential at point $ b $?**Answer:**\[ V_b = -5.27 \times 10^5 \, \text{V} \]### Explanation:**Correct**Given:\[ r_{b1} = 0.0141 \, \text{m}, \, r_{b2} = 0.0100 \, \text{m} \]Calculate:\[ V_b = k\left(\frac{q_1}{r_{b1}} + \frac{q_2}{r_{b2}}\right) \]Using:\[ k = 8.99 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2 \]\[ V_b = (8.99 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2) \left(\frac{+2.00 \times 10^{-6} \, \text{C}}{0.0141 \, \text{m}} + \frac{-2.00 \times 10^{-6} \, \text{C}}{0. Point charges $ q_1 = +2.00 \, \mu \text{C} $ and $ q_2 = -2.00 \, \mu \text{C} $ are placed at adjacent corners of a square for which the length of each side is 1.00 cm. Point $ a $ is at the center of the square, and point $ b $ is at the empty corner closest to $ q_2 $. Take the electric potential to be zero at a distance far from both charges.

We know the work is done on a charge q to move from position a to b isWhere: is potential at…

Answered: Part C: A point charge q3 = -5.00 μC…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Part C: A point charge q3 = -5.00 μC moves from point a to point b. How much work is done on q3 by the electric forces exerted by q1 and q2?

Express your answer with the appropriate units.

W_ab=__

## Part A

**Question:**
What is the electric potential at point $ a $ due to $ q_1 $ and $ q_2 $?

**Answer:**
\[ V_a = 0 \, \text{V} \]

### Explanation:

**Correct**

**IDENTIFY:** The potential at any point is the scalar sum of the potentials due to individual charges.

**SET UP:**
\[ V = kq/r \]
\[ W_{ab} = q(V_a - V_b) \]

**EXECUTE:**
\[ r_{a1} = r_{a2} = \frac{1}{2} \sqrt{(0.0100 \, \text{m})^2 + (0.0100 \, \text{m})^2} = 0.0071 \, \text{m} \]

\[ V_a = k\left(\frac{q_1}{r_{a1}} + \frac{q_2}{r_{a2}}\right) = 0 \, \text{V} \]

---

## Part B

**Question:**
What is the electric potential at point $ b $?

**Answer:**
\[ V_b = -5.27 \times 10^5 \, \text{V} \]

### Explanation:

**Correct**

Given:
\[ r_{b1} = 0.0141 \, \text{m}, \, r_{b2} = 0.0100 \, \text{m} \]

Calculate:
\[ V_b = k\left(\frac{q_1}{r_{b1}} + \frac{q_2}{r_{b2}}\right) \]

Using:
\[ k = 8.99 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2 \]

\[ V_b = (8.99 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2) \left(\frac{+2.00 \times 10^{-6} \, \text{C}}{0.0141 \, \text{m}} + \frac{-2.00 \times 10^{-6} \, \text{C}}{0.

Point charges $ q_1 = +2.00 \, \mu \text{C} $ and $ q_2 = -2.00 \, \mu \text{C} $ are placed at adjacent corners of a square for which the length of each side is 1.00 cm. Point $ a $ is at the center of the square, and point $ b $ is at the empty corner closest to $ q_2 $. Take the electric potential to be zero at a distance far from both charges.

Expert Solution

Step 1: Work is done on a charge

We know the work is done on a charge q to move from position a to b is

$straight W subscript ab equals straight q left parenthesis straight V subscript straight a minus straight V subscript straight b right parenthesis$

Where:

$straight V subscript straight a$ is potential at position a, and $straight V subscript straight b$ is potential at position b.

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Part C: A point charge q3 = -5.00 μC moves from point a to point b. How much work is done on q3 by the electric forces exerted by q1 and q2? Express your answer with the appropriate units. Wab=__