Coulomb's Law Worksheet Answers Explained Simply
Table of Contents :
Coulomb's Law is a fundamental principle in electrostatics that describes the force between two charged objects. It states that the magnitude of the electrostatic 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. In this article, we'll break down Coulomb's Law and provide a clear explanation of worksheet answers related to it. 💡
Understanding Coulomb's Law
Coulomb's Law can be expressed mathematically as:
[ F = k \frac{|q_1 \cdot q_2|}{r^2} ]
Where:
- ( F ) = force between the charges (in Newtons)
- ( k ) = Coulomb's constant (( 8.99 \times 10^9 , N , m^2/C^2 ))
- ( q_1 ) and ( q_2 ) = the amounts of the charges (in Coulombs)
- ( r ) = distance between the charges (in meters)
Key Concepts to Note
- Like Charges Repel: If both charges are positive or both are negative, they will repel each other. This means the force ( F ) will be positive.
- Opposite Charges Attract: If one charge is positive and the other is negative, they will attract each other, leading to a negative force ( F ).
- Distance Matters: As the distance ( r ) increases, the force ( F ) between the charges decreases rapidly due to the ( r^2 ) term in the denominator. This highlights the importance of distance in electrostatic interactions.
Worksheets: Common Problems and Their Solutions
Coulomb's Law worksheets typically contain problems involving calculations of the forces between charged objects. Below, we provide examples of common problems and their answers explained simply.
Example Problem 1: Calculating the Force Between Two Charges
Problem: Calculate the force between two charges, ( q_1 = 5 , \mu C ) and ( q_2 = -3 , \mu C ), that are ( 0.1 , m ) apart.
Solution:
-
Convert the microcoulombs to coulombs:
( q_1 = 5 , \mu C = 5 \times 10^{-6} , C )
( q_2 = -3 , \mu C = -3 \times 10^{-6} , C ) -
Use Coulomb's Law:
[ F = k \frac{|q_1 \cdot q_2|}{r^2} ]
[ F = (8.99 \times 10^9) \frac{|(5 \times 10^{-6}) \cdot (-3 \times 10^{-6})|}{(0.1)^2} ]
[ F = (8.99 \times 10^9) \frac{15 \times 10^{-12}}{0.01} ]
[ F = (8.99 \times 10^9) \cdot (1.5 \times 10^{-9}) ]
[ F = 13.485 , N ]
- Important Note: The force is attractive because the charges are of opposite signs. Thus, we state the answer as ( F = -13.485 , N ) indicating direction.
Example Problem 2: Effect of Distance on Force
Problem: What happens to the force if the distance between two charges is doubled?
Solution:
- Let's denote the original distance as ( r ) and the new distance as ( 2r ).
- According to Coulomb's Law: [ F' = k \frac{|q_1 \cdot q_2|}{(2r)^2} = k \frac{|q_1 \cdot q_2|}{4r^2} = \frac{1}{4} \left( k \frac{|q_1 \cdot q_2|}{r^2} \right) = \frac{F}{4} ]
- Conclusion: When the distance is doubled, the force reduces to a quarter of its original value.
Example Problem 3: Combining Charges
Problem: Two point charges of ( 2 , \mu C ) and ( 4 , \mu C ) are ( 0.5 , m ) apart. What is the force between them?
Solution:
-
Convert to Coulombs:
( q_1 = 2 , \mu C = 2 \times 10^{-6} , C )
( q_2 = 4 , \mu C = 4 \times 10^{-6} , C ) -
Apply Coulomb’s Law:
[ F = k \frac{|q_1 \cdot q_2|}{r^2} ]
[ F = (8.99 \times 10^9) \frac{|(2 \times 10^{-6}) \cdot (4 \times 10^{-6})|}{(0.5)^2} ]
[ F = (8.99 \times 10^9) \frac{8 \times 10^{-12}}{0.25} ]
[ F = (8.99 \times 10^9) \cdot (32 \times 10^{-12}) ]
[ F = 287.68 , N ]
Summary Table of Forces
Here's a simple table summarizing the results of the calculations for various scenarios:
<table> <tr> <th>Charges (C)</th> <th>Distance (m)</th> <th>Force (N)</th> <th>Type of Force</th> </tr> <tr> <td>5 µC, -3 µC</td> <td>0.1</td> <td>-13.485</td> <td>Attractive</td> </tr> <tr> <td>2 µC, 4 µC</td> <td>0.5</td> <td>287.68</td> <td>Repulsive</td> </tr> </table>
Conclusion
Understanding Coulomb's Law is essential for students and anyone interested in the field of physics, especially electrostatics. The calculations may appear complex at first, but breaking them down into manageable steps makes them much easier to handle. By practicing similar problems on worksheets and understanding their solutions, you can solidify your grasp of the forces at play between charged objects. Keep exploring and practicing, and you'll become adept at using Coulomb's Law in no time! 🌟