Coulomb's Law Worksheet Answers: Quick And Easy Guide
Table of Contents :
Coulomb's Law is a fundamental principle in electrostatics that describes the force between two charged objects. Whether you're studying physics in school or simply want to brush up on your understanding of electric forces, this guide aims to provide you with a comprehensive overview of Coulomb's Law, including key concepts, formulas, and solutions to common problems. 📚⚡
Understanding Coulomb's Law
Coulomb's Law states that the 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 law can be mathematically represented as:
[ F = k \frac{|q_1 \cdot q_2|}{r^2} ]
where:
- ( F ) is the magnitude of 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 centers of the two charges (in meters).
Key Concepts of Coulomb's Law
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Direction of Force: The force is attractive if the charges are of opposite signs (one positive and one negative) and repulsive if they are of the same sign (both positive or both negative). This indicates that like charges repel and unlike charges attract. 🔄
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Magnitude of Force: The strength of the force depends on the magnitude of the charges and the distance between them. Larger charges will produce a stronger force, while increasing the distance will decrease the force significantly.
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Superposition Principle: When multiple charges are present, the total force on any charge is the vector sum of the forces exerted on it by all other charges. This requires considering both the magnitudes and the directions of the forces involved. 🧮
Coulomb's Law Worksheet Problems
To help you apply what you've learned, below is a sample worksheet with common problems related to Coulomb's Law. The answers will also be provided for quick reference.
Problem 1: Calculating Force Between Two Charges
Question: Calculate the force between two charges, ( q_1 = 3 , \mu C ) and ( q_2 = -5 , \mu C ), that are ( 0.2 , m ) apart.
Solution:
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Convert microcoulombs to coulombs:
- ( q_1 = 3 \times 10^{-6} , C )
- ( q_2 = -5 \times 10^{-6} , C )
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Use Coulomb's Law: [ F = k \frac{|q_1 \cdot q_2|}{r^2} ] [ F = (8.99 \times 10^9) \cdot \frac{|3 \times 10^{-6} \cdot -5 \times 10^{-6}|}{(0.2)^2} ] [ F = (8.99 \times 10^9) \cdot \frac{15 \times 10^{-12}}{0.04} ] [ F = (8.99 \times 10^9) \cdot (3.75 \times 10^{-10}) ] [ F \approx 3.37 , N \text{ (attractive)} ]
Problem 2: Effect of Distance on Force
Question: If the distance between two charges is doubled, how does the force change?
Solution:
Using Coulomb's Law, if ( r ) is doubled, the new force ( F' ) will be:
[ F' = k \frac{|q_1 \cdot q_2|}{(2r)^2} = k \frac{|q_1 \cdot q_2|}{4r^2} = \frac{F}{4} ]
Thus, the force is reduced to one-quarter of its original value.
Sample Worksheet Table
Here’s a quick reference table for solving Coulomb's Law problems:
<table> <tr> <th>Problem Number</th> <th>Charges (C)</th> <th>Distance (m)</th> <th>Force (N)</th> </tr> <tr> <td>1</td> <td>3 μC, -5 μC</td> <td>0.2</td> <td>3.37 (attractive)</td> </tr> <tr> <td>2</td> <td>4 μC, 4 μC</td> <td>0.5</td> <td>0.144</td> </tr> </table>
Important Notes
“Coulomb's Law applies strictly to point charges and does not account for the distribution of charge in real-world objects. Always consider the approximations made when applying this law.”
Conclusion
Coulomb's Law is essential for understanding the interactions between charged particles. By mastering this concept and practicing related problems, you can deepen your understanding of electrostatics and its applications in real life. Remember to analyze the situation carefully, apply the correct formulas, and think about how various factors affect the forces involved. With practice, solving Coulomb's Law problems will become quick and easy! 🚀