Coulomb's Law Worksheet Answer Key: Your Essential Guide
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Coulomb's Law is a fundamental principle in physics that describes the force between charged particles. If you are currently studying electrostatics or preparing for an exam, understanding Coulomb's Law and practicing problems is crucial for your success. In this article, we’ll provide a comprehensive guide to Coulomb's Law, including a breakdown of its equation, examples of problems you may encounter, and an answer key to help you check your understanding. Let’s dive into this essential topic! ⚡️
What is Coulomb's Law?
Coulomb's Law quantifies the force between two charged objects. It states that the force (F) between two point charges is directly proportional to the product of the magnitudes of the charges (q1 and q2) and inversely proportional to the square of the distance (r) between them. The formula can be written as:
[ F = k \cdot \frac{|q_1 \cdot q_2|}{r^2} ]
Where:
- ( F ) = the magnitude of the electrostatic force between the charges (in Newtons)
- ( k ) = Coulomb's constant ((8.99 \times 10^9 , \text{N m}^2/\text{C}^2))
- ( q_1 ) and ( q_2 ) = the magnitudes of the charges (in Coulombs)
- ( r ) = the distance between the charges (in meters)
Key Points to Remember
- Like Charges Repel: If both charges are positive or both are negative, the force is repulsive.
- Opposite Charges Attract: If one charge is positive and the other is negative, the force is attractive.
- Vector Nature of Force: The direction of the force is important and should be considered when solving problems.
Sample Problems Involving Coulomb's Law
Let’s look at a few examples to illustrate the application of Coulomb's Law.
Problem 1: Calculate the Force Between Two Charges
Given:
- Charge ( q_1 = 3 , \mu C = 3 \times 10^{-6} , C )
- Charge ( q_2 = -2 , \mu C = -2 \times 10^{-6} , C )
- Distance ( r = 0.5 , m )
Solution: Using the formula, the force is calculated as follows:
[ F = k \cdot \frac{|q_1 \cdot q_2|}{r^2} ]
Substituting the values:
[ F = 8.99 \times 10^9 \cdot \frac{|(3 \times 10^{-6}) \cdot (-2 \times 10^{-6})|}{(0.5)^2} ]
Calculating this gives:
[ F = 8.99 \times 10^9 \cdot \frac{6 \times 10^{-12}}{0.25} = 2.156 , N ]
Problem 2: Determining the Distance Between Charges
Given:
- Charge ( q_1 = 5 , \mu C )
- Charge ( q_2 = 5 , \mu C )
- Force ( F = 1 , N )
Solution: We need to find the distance ( r ). Rearranging Coulomb's Law formula gives:
[ r = \sqrt{k \cdot \frac{|q_1 \cdot q_2|}{F}} ]
Substituting the values:
[ r = \sqrt{8.99 \times 10^9 \cdot \frac{|(5 \times 10^{-6}) \cdot (5 \times 10^{-6})|}{1}} ]
Calculating this will yield:
[ r \approx 0.141 , m ]
Coulomb's Law Worksheet Answer Key
Here is a helpful answer key for a Coulomb's Law worksheet that may contain various problems. Use this key to check your work and ensure you understand the concepts involved.
<table> <tr> <th>Problem Number</th> <th>Answer</th> </tr> <tr> <td>1</td> <td>2.156 N</td> </tr> <tr> <td>2</td> <td>0.141 m</td> </tr> <tr> <td>3</td> <td>1.802 N</td> </tr> <tr> <td>4</td> <td>0.1 m</td> </tr> <tr> <td>5</td> <td>3.9 N</td> </tr> </table>
Important Notes
“Always remember to pay attention to the units you are using. Converting microcoulombs to coulombs or centimeters to meters is essential to getting the correct answer.”
Practical Applications of Coulomb's Law
Understanding Coulomb's Law is not just academic; it has real-world applications, including:
- Electrostatic Precipitators: Used in industrial processes to remove particles from exhaust gases.
- Capacitors: Devices that store electrical energy based on the principles of electrostatics.
- Atomic and Molecular Physics: Understanding the forces between particles helps to explain chemical bonding and reactions.
Conclusion
Coulomb's Law is a fundamental concept that underpins much of the study in physics, particularly in electrostatics. By mastering the equations and problem-solving techniques associated with this law, you'll develop a solid foundation for understanding more complex topics in physics. Regular practice, along with reference to resources like worksheets and answer keys, will further enhance your comprehension. Happy studying! 📚