Coulomb Force Calculation Find Net Force On Q2 Explained
Hey guys! Let's dive into this fascinating physics problem involving Coulomb's Law. We've got three charges lined up, and we need to figure out the force acting on the middle charge. It sounds a bit intimidating at first, but trust me, we'll break it down step by step so it becomes super clear. Let's get started!
Understanding the Problem
Before we jump into calculations, let's make sure we fully grasp what's going on. We have three charges: Q₁, Q₂, and Q₃. Q₁ has a charge of 20μC (microcoulombs), Q₂ has a charge of -10μC, and Q₃ has a charge of 40μC. These charges are arranged in a straight line, which makes our lives a little easier. The distance between each charge is given as d = 20 cm. The big question we're trying to answer is: what is the magnitude and direction of the Coulomb force acting on Q₂?
Coulomb's Law is the key here. It tells us that the force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. Remember, opposite charges attract, and like charges repel. This is crucial for figuring out the direction of the forces.
To solve this, we'll need to calculate the force between Q₁ and Q₂ (let's call it F₁₂) and the force between Q₂ and Q₃ (let's call it F₂₃). Since forces are vectors, we'll need to consider their directions as well. Once we have these two forces, we can add them together to find the net force acting on Q₂. This net force will tell us both the magnitude and the direction of the force.
Now, let's put on our thinking caps and start crunching some numbers! We'll go through each calculation step by step, so you can follow along easily. Don't worry if it seems a bit complex at first; we'll make it super clear!
Calculating the Force Between Q₁ and Q₂ (F₁₂)
Okay, first things first, let's calculate the force between Q₁ and Q₂ (F₁₂). This is where Coulomb's Law really shines. Remember the formula? It's:
F = k * |Q₁ * Q₂| / r²
Where:
- F is the force between the charges
- k is Coulomb's constant (approximately 8.99 × 10⁹ N⋅m²/C²)
- Q₁ and Q₂ are the magnitudes of the charges
- r is the distance between the charges
Let's plug in the values we know:
- Q₁ = 20μC = 20 × 10⁻⁶ C
- Q₂ = -10μC = -10 × 10⁻⁶ C
- r = d = 20 cm = 0.2 m
- k = 8.99 × 10⁹ N⋅m²/C²
So, the equation becomes:
F₁₂ = (8.99 × 10⁹ N⋅m²/C²) * |(20 × 10⁻⁶ C) * (-10 × 10⁻⁶ C)| / (0.2 m)²
Now, let's do the math. First, calculate the product of the charges:
|(20 × 10⁻⁶ C) * (-10 × 10⁻⁶ C)| = 200 × 10⁻¹² C²
Next, square the distance:
(0.2 m)² = 0.04 m²
Now, plug these back into the equation:
F₁₂ = (8.99 × 10⁹ N⋅m²/C²) * (200 × 10⁻¹² C²) / (0.04 m²)
F₁₂ = (8.99 × 10⁹) * (200 × 10⁻¹²) / 0.04 N
F₁₂ = 17.98 × 10⁻¹ / 0.04 N
F₁₂ = 4.495 N
So, the magnitude of the force between Q₁ and Q₂ is 4.495 N. But what about the direction? Remember, Q₁ is positive, and Q₂ is negative. Opposite charges attract, so Q₂ will be pulled towards Q₁. Therefore, F₁₂ is a force of 4.495 N directed towards Q₁.
We've nailed the first part! Now, let's move on to calculating the force between Q₂ and Q₃. We'll use the same principles, so you'll see how it all comes together. Keep up the great work!
Calculating the Force Between Q₂ and Q₃ (F₂₃)
Alright, let's tackle the force between Q₂ and Q₃ (F₂₃). We're going to use the same Coulomb's Law formula as before, which is:
F = k * |Q₁ * Q₂| / r²
This time, our charges are Q₂ and Q₃, and the distance between them is still d = 20 cm = 0.2 m. Let's plug in the values:
- Q₂ = -10μC = -10 × 10⁻⁶ C
- Q₃ = 40μC = 40 × 10⁻⁶ C
- r = d = 0.2 m
- k = 8.99 × 10⁹ N⋅m²/C²
So, our equation looks like this:
F₂₃ = (8.99 × 10⁹ N⋅m²/C²) * |(-10 × 10⁻⁶ C) * (40 × 10⁻⁶ C)| / (0.2 m)²
Let's break it down step by step. First, calculate the product of the charges:
|(-10 × 10⁻⁶ C) * (40 × 10⁻⁶ C)| = 400 × 10⁻¹² C²
Next, we already know the square of the distance from our previous calculation:
(0.2 m)² = 0.04 m²
Now, plug these values back into the equation:
F₂₃ = (8.99 × 10⁹ N⋅m²/C²) * (400 × 10⁻¹² C²) / (0.04 m²)
F₂₃ = (8.99 × 10⁹) * (400 × 10⁻¹²) / 0.04 N
F₂₃ = 35.96 × 10⁻¹ / 0.04 N
F₂₃ = 8.99 N
So, the magnitude of the force between Q₂ and Q₃ is 8.99 N. Now, let's figure out the direction. Q₂ is negative, and Q₃ is positive, so they attract each other. This means Q₂ will be pulled towards Q₃. Therefore, F₂₃ is a force of 8.99 N directed towards Q₃.
Awesome! We've calculated the force between Q₂ and Q₃. Now we have both F₁₂ and F₂₃. The next step is to combine these forces to find the net force acting on Q₂. We're getting closer to the final answer!
Finding the Net Force on Q₂
Okay, we're in the home stretch! We've calculated the two forces acting on Q₂: F₁₂ (the force due to Q₁) and F₂₃ (the force due to Q₃). Now, we need to find the net force acting on Q₂. Since these forces are acting along the same line, we can simply add them together, keeping their directions in mind.
We found that:
- F₁₂ = 4.495 N directed towards Q₁
- F₂₃ = 8.99 N directed towards Q₃
Since Q₁ and Q₃ are on opposite sides of Q₂, these forces are acting in opposite directions. We need to choose a convention for positive and negative directions. Let's say that a force directed towards Q₃ is positive, and a force directed towards Q₁ is negative. This means:
- F₂₃ = +8.99 N
- F₁₂ = -4.495 N
The net force (Fnet) on Q₂ is the sum of these two forces:
Fnet = F₁₂ + F₂₃
Fnet = -4.495 N + 8.99 N
Fnet = 4.495 N
So, the net force acting on Q₂ is 4.495 N. And what about the direction? Since our result is positive, this means the net force is directed towards Q₃.
We've done it! We've calculated both the magnitude and the direction of the net force acting on Q₂. This problem might have seemed tricky at first, but by breaking it down step by step and using Coulomb's Law, we were able to solve it. Great job, everyone!
Final Answer and Conclusion
Let's recap what we've found. We calculated the net Coulomb force acting on charge Q₂ to be 4.495 N directed towards Q₃. This means Q₂ experiences a force pulling it in the direction of Q₃ due to the combined effects of the attractive force from Q₃ and the repulsive force from Q₁.
Coulomb's Law is a fundamental concept in physics, and understanding how to apply it is crucial for solving problems involving electric charges. We've seen how to calculate the force between two charges, and how to combine multiple forces to find the net force. This approach can be used for more complex scenarios as well.
I hope this explanation has been helpful and has made the concept of Coulomb's Law a little clearer. If you have any more questions or want to explore other physics problems, feel free to ask! Keep up the great work, and happy learning!
Therefore, the correct answer is approximately 4.5 N towards Q₃.
Additional Practice
To really solidify your understanding, try working through similar problems. For example, you could change the magnitudes of the charges, the distances between them, or even add more charges to the system. Each time you solve a problem, you'll become more comfortable with Coulomb's Law and its applications.
You can also explore how Coulomb's Law relates to other concepts in electromagnetism, such as electric fields and electric potential. These concepts build upon the foundation of Coulomb's Law and will give you a deeper understanding of how electric charges interact.
Remember, physics is all about practice. The more you practice, the better you'll become at solving problems and understanding the underlying principles. So, keep exploring, keep questioning, and keep learning!
Calculate the magnitude and direction of the Coulomb force acting on charge Q₂ given the charges Q₁ = 20μC, Q₂ = -10μC, and Q₃ = 40μC are arranged in a straight line with a distance d = 20 cm between each charge.
Coulomb Force Calculation Find Net Force on Q2 Explained
