Coulomb's Law Worksheet Answer Key: Quick Guide
Table of Contents :
Coulomb's Law is a fundamental principle in physics that describes the interaction between electrically charged particles. In this guide, we will explore Coulomb's Law, provide example problems, and offer a worksheet answer key to help you understand the applications of this important concept.
Understanding Coulomb's Law ⚡
Coulomb's Law quantifies the electrostatic force between two charges. According to this law, the force between two point charges is directly proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. The formula can be expressed as:
[ F = k \cdot \frac{|q_1 \cdot q_2|}{r^2} ]
Where:
- ( F ) is the magnitude of the electrostatic force (in Newtons),
- ( k ) is Coulomb's constant (( 8.99 \times 10^9 , \text{N m}^2/\text{C}^2 )),
- ( q_1 ) and ( q_2 ) are the amounts of the charges (in Coulombs),
- ( r ) is the distance between the centers of the two charges (in meters).
Key Points to Remember:
- Opposite Charges Attract: If one charge is positive and the other negative, they will attract each other.
- Like Charges Repel: If both charges are either positive or negative, they will repel each other.
- Distance Matters: The force decreases rapidly as the distance between the charges increases.
Example Problems 📚
To understand how to apply Coulomb's Law, let's walk through some example problems and provide a worksheet format that you can use for practice.
Example Problem 1
Question: What is the force between two charges, +2 μC and -3 μC, separated by a distance of 0.5 meters?
Solution:
- Convert microcoulombs to coulombs:
- ( q_1 = 2 \times 10^{-6} , \text{C} )
- ( q_2 = -3 \times 10^{-6} , \text{C} )
- Use Coulomb's Law: [ F = k \cdot \frac{|q_1 \cdot q_2|}{r^2} = 8.99 \times 10^9 \cdot \frac{|2 \times 10^{-6} \cdot -3 \times 10^{-6}|}{(0.5)^2} ]
- Calculate the force: [ F = 8.99 \times 10^9 \cdot \frac{6 \times 10^{-12}}{0.25} = 215.76 , \text{N} ]
Example Problem 2
Question: Calculate the force between two charges of +4 μC and +5 μC that are 2 meters apart.
Solution:
- Convert microcoulombs to coulombs:
- ( q_1 = 4 \times 10^{-6} , \text{C} )
- ( q_2 = 5 \times 10^{-6} , \text{C} )
- Use Coulomb's Law: [ F = k \cdot \frac{|q_1 \cdot q_2|}{r^2} = 8.99 \times 10^9 \cdot \frac{(4 \times 10^{-6} \cdot 5 \times 10^{-6})}{(2)^2} ]
- Calculate the force: [ F = 8.99 \times 10^9 \cdot \frac{20 \times 10^{-12}}{4} = 44.95 , \text{N} ]
Coulomb's Law Worksheet 📑
Here's a sample worksheet you can use to practice applying Coulomb's Law. Fill in your answers based on the examples above.
| Problem | Charge 1 (C) | Charge 2 (C) | Distance (m) | Force (N) |
|---|---|---|---|---|
| 1 | +3 μC | -4 μC | 1.5 | |
| 2 | +1 μC | +1 μC | 0.5 | |
| 3 | -2 μC | +5 μC | 3 | |
| 4 | +6 μC | +2 μC | 1 | |
| 5 | -7 μC | -1 μC | 4 |
Note: Remember to convert microcoulombs to coulombs for your calculations!
Answer Key for Worksheet 📊
Here is the answer key to the worksheet provided above. Use it to check your answers and understand any mistakes.
<table> <tr> <th>Problem</th> <th>Charge 1 (C)</th> <th>Charge 2 (C)</th> <th>Distance (m)</th> <th>Force (N)</th> </tr> <tr> <td>1</td> <td>+3 μC</td> <td>-4 μC</td> <td>1.5</td> <td>~7.99</td> </tr> <tr> <td>2</td> <td>+1 μC</td> <td>+1 μC</td> <td>0.5</td> <td>35.96</td> </tr> <tr> <td>3</td> <td>-2 μC</td> <td>+5 μC</td> <td>3</td> <td>~9.98</td> </tr> <tr> <td>4</td> <td>+6 μC</td> <td>+2 μC</td> <td>1</td> <td>107.94</td> </tr> <tr> <td>5</td> <td>-7 μC</td> <td>-1 μC</td> <td>4</td> <td>~4.46</td> </tr> </table>
Conclusion
Coulomb's Law plays a vital role in understanding the forces between charged particles. By practicing with the worksheet and reviewing the answer key, you can strengthen your grasp of this essential concept in physics. Whether you're preparing for exams or just looking to enhance your knowledge, mastering Coulomb's Law will be beneficial in your academic journey. Remember to always keep the core principles in mind and practice regularly!