Coulomb's Law Worksheet Answer Key For Easy Learning
Table of Contents :
Coulomb's Law is a fundamental principle in electrostatics that describes the force between two charged objects. This law is essential for students and professionals alike to understand the interactions of electrical charges. In this article, we will explore Coulomb's Law in detail, provide some practical examples, and include a worksheet answer key to facilitate easy learning. Let’s dive in! ⚡️
What is Coulomb's Law?
Coulomb's Law states that the magnitude of the electrostatic force ( F ) between two point charges is directly proportional to the product of the magnitudes of the charges ( q_1 ) and ( q_2 ), and inversely proportional to the square of the distance ( r ) between them. The formula can be expressed as:
[ F = k \frac{|q_1 \cdot q_2|}{r^2} ]
Where:
- ( F ) is the force between the charges (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 charges (in meters)
Key Concepts of Coulomb's Law
1. Nature of Charges
- Like Charges: Repel each other (e.g., positive-positive or negative-negative).
- Opposite Charges: Attract each other (e.g., positive-negative).
2. Distance and Force
The electrostatic force diminishes rapidly with increasing distance. Doubling the distance decreases the force by a factor of four due to the square relationship in the formula.
3. Coulomb's Constant
Coulomb's constant ( k ) is vital as it determines the strength of the electrostatic force in a vacuum.
Example Problems
To aid your understanding, here are a few example problems along with their solutions.
Example 1: Two Positive Charges
Problem: Calculate the force between two charges of ( +2 , \mu C ) and ( +3 , \mu C ) placed ( 0.5 , m ) apart.
Solution:
- Convert microcoulombs to coulombs:
- ( q_1 = 2 \times 10^{-6} , C )
- ( q_2 = 3 \times 10^{-6} , C )
- Use Coulomb's Law: [ F = k \frac{|q_1 \cdot q_2|}{r^2} = 8.99 \times 10^9 \frac{|2 \times 10^{-6} \cdot 3 \times 10^{-6}|}{(0.5)^2} ] [ F = 8.99 \times 10^9 \frac{6 \times 10^{-12}}{0.25} = 8.99 \times 10^9 \times 2.4 \times 10^{-11} = 215.76 , N ]
Example 2: Opposite Charges
Problem: Determine the force between ( +1 , \mu C ) and ( -1 , \mu C ) charges that are ( 0.2 , m ) apart.
Solution:
- Charges in coulombs:
- ( q_1 = 1 \times 10^{-6} , C )
- ( q_2 = -1 \times 10^{-6} , C )
- Use Coulomb's Law: [ F = k \frac{|1 \times 10^{-6} \cdot -1 \times 10^{-6}|}{(0.2)^2} ] [ F = 8.99 \times 10^9 \frac{1 \times 10^{-12}}{0.04} = 224.75 , N ]
Coulomb's Law Worksheet
A worksheet is an excellent tool for practicing the application of Coulomb's Law. Below is a table to structure your worksheet.
<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>+1 µC</td> <td>+2 µC</td> <td>0.3</td> <td>Calculate</td> </tr> <tr> <td>2</td> <td>-3 µC</td> <td>+4 µC</td> <td>0.1</td> <td>Calculate</td> </tr> <tr> <td>3</td> <td>+5 µC</td> <td>-6 µC</td> <td>0.5</td> <td>Calculate</td> </tr> <tr> <td>4</td> <td>-2 µC</td> <td>-2 µC</td> <td>0.7</td> <td>Calculate</td> </tr> </table>
Answer Key
- Problem 1: ( 199.65 , N )
- Problem 2: ( 107.48 , N )
- Problem 3: ( 107.38 , N )
- Problem 4: ( 51.01 , N )
Note: Make sure to apply the concepts of attraction and repulsion while solving the problems.
Conclusion
Coulomb's Law is an essential concept in understanding electrostatic forces between charged particles. Through this guide and the provided worksheet, learners can enhance their understanding and application of this fundamental law. With practice, mastering Coulomb's Law will become a straightforward process, providing a solid foundation for further studies in physics and electrical engineering. Remember, hands-on practice is the key to success! 🌟