Calculating Electric Force: A Step-by-Step Guide

Dec 4, 2025 by Tom Lembong 49 views

Hey there, physics enthusiasts! Today, we're diving into the fascinating world of electrostatics. Specifically, we're going to learn how to determine the magnitude of the resulting electric force acting on a charge within a system of multiple charges. Sounds complex? Don't sweat it! I'll break it down into easy-to-follow steps. We'll be working with a classic problem involving three charges (q1, q2, and q3), and our goal is to figure out the net force on q3. Let's get started, shall we?

Understanding the Basics: Coulomb's Law and Electric Forces

Alright, before we jump into the problem, let's brush up on the fundamental principles. The cornerstone of our calculation is Coulomb's Law. This law tells us how much force exists between two charged particles. The force, denoted as F, 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 is:

F = k * |q1 * q2| / r²

Where:

F is the electric force (measured in Newtons, N)
k is Coulomb's constant (approximately 8.9875 × 10⁹ N⋅m²/C²)
q1 and q2 are the magnitudes of the charges (measured in Coulombs, C)
r is the distance between the charges (measured in meters, m)

Now, a couple of key points to remember: Electric forces are vector quantities. This means they have both magnitude (size) and direction. The direction of the force depends on the signs of the charges:

Like charges repel each other. If q1 and q2 have the same sign (both positive or both negative), the force between them is repulsive, and they push away from each other.
Opposite charges attract each other. If q1 and q2 have opposite signs (one positive and one negative), the force between them is attractive, and they pull towards each other.

In our problem, we will have to consider the forces of both attraction and repulsion, since our charges have different signs. We're going to calculate the force exerted on one charge due to the presence of other charges.

Applying Coulomb's Law: Force on a Specific Charge

Let's apply this to our problem. We have three charges, and we want to find the total force on q3. This means we must consider the force exerted on q3 by q1 and the force exerted on q3 by q2. These individual forces, F13 and F23, will then be added together (as vectors!) to find the net force on q3.

To do this systematically, we will follow these steps:

Identify the charges and distances. First, we need to know the values of our charges (q1, q2, and q3) and the distances between them. The problem will usually provide these values. If the distances are not explicitly given, you will need to determine them from the geometry of the situation.
Calculate the force between each pair of charges. Using Coulomb's Law, calculate the magnitude of the force F13 that q1 exerts on q3 and the magnitude of the force F23 that q2 exerts on q3. Remember to consider the absolute values of the charges when calculating the magnitude.
Determine the direction of each force. Based on the signs of the charges, determine whether each force is attractive (charges of opposite signs) or repulsive (charges of the same sign).
Resolve forces into components. If the forces are not acting along the same line (which is often the case in 2D or 3D problems), resolve them into their x and y (or other appropriate) components.
Calculate the net force. Add the force components to find the x and y components of the net force on q3. Then, use the Pythagorean theorem to calculate the magnitude of the net force.

Detailed Solution: Step-by-Step Calculation of Electric Force

Okay, let's put this into practice using the information provided. The problem specifies:

q1 = +4 μC = +4 × 10⁻⁶ C (micro Coulombs, remember to convert to Coulombs)
q2 = -5 μC = -5 × 10⁻⁶ C
q3 = -6 μC = -6 × 10⁻⁶ C

And let's assume the following distances (these will be provided in the problem, but we'll use example values for illustration):

Distance between q1 and q3 (r13) = 0.20 m
Distance between q2 and q3 (r23) = 0.30 m

Now, follow these steps.

Step 1: Calculate F13

We will use Coulomb's Law to calculate the force exerted by q1 on q3 (F13):

F13 = k * |q1 * q3| / r13² F13 = (8.9875 × 10⁹ N⋅m²/C²) * |(4 × 10⁻⁶ C) * (-6 × 10⁻⁶ C)| / (0.20 m)² F13 = (8.9875 × 10⁹) * (24 × 10⁻¹²) / 0.04 F13 ≈ 5.39 N

Since q1 is positive and q3 is negative, the force F13 is attractive. This means q1 pulls q3 toward itself.

Step 2: Calculate F23

Now we calculate the force exerted by q2 on q3 (F23):

F23 = k * |q2 * q3| / r23² F23 = (8.9875 × 10⁹ N⋅m²/C²) * |(-5 × 10⁻⁶ C) * (-6 × 10⁻⁶ C)| / (0.30 m)² F23 = (8.9875 × 10⁹) * (30 × 10⁻¹²) / 0.09 F23 ≈ 3.00 N

Since q2 is negative and q3 is negative, the force F23 is repulsive. This means q2 pushes q3 away from itself.

Step 3: Determine the Direction and Find the Net Force

In this example, let's assume all the charges are on a straight line, like this: q1--q3--q2 (q3 is located in between q1 and q2). F13 acts to the left (attraction), while F23 acts to the right (repulsion). The net force on q3 is the vector sum of these forces. Because they are on the same line, the total force is:

Fnet = F23 - F13 Fnet = 3.00 N - 5.39 N = -2.39 N

The negative sign indicates that the net force is in the direction of F13, or to the left. The magnitude of the net force is 2.39 N.

Example with Angles

Let's consider a slightly more complex situation where the charges are not all along a straight line. Suppose q1 is at the origin (0,0), q2 is on the x-axis at (0.3,0), and q3 is at (0.2,0.2). This forms a triangle.

Calculate the distances: We already know r13 = 0.2 m. We need to calculate the distance r23. Using the distance formula: r23 = √((0.3-0.2)² + (0-0.2)²) ≈ 0.22 m
Calculate F13 and F23 (as before): F13 ≈ 5.39 N (attractive, towards q1) F23 ≈ 3.00 N (repulsive, away from q2)
Resolve into components: The angle between the x-axis and the line connecting q1 and q3 is θ = 45 degrees, as the coordinates form an isosceles triangle. F13 acts at an angle of 45 degrees relative to the horizontal.

F13x = -5.39 * cos(45) ≈ -3.81 N F13y = -5.39 * sin(45) ≈ -3.81 N

For F23, we need to calculate the angle that connects q3 and q2. With q2 in the position (0.3,0) and q3 in (0.2,0.2), we find that the force is not aligned with either the x or y-axis. The angle will be different.

F23x = 3.00 * cos(θ) F23y = 3.00 * sin(θ)

After calculating the appropriate angles for F23 you can then calculate F23x and F23y.

Net Force: Fnetx = F13x + F23x Fnety = F13y + F23y

Finally, calculate the magnitude of the net force: Fnet = √(Fnetx² + Fnety²)

Tips and Tricks for Solving Electric Force Problems

Alright, here are some helpful hints to keep in mind when tackling these types of problems:

Units are your friend. Always use consistent units (SI units: Coulombs, meters, Newtons). Double-check your conversions to avoid errors.
Draw a diagram. This is super important. Visualizing the problem with a diagram helps you determine the directions of the forces and avoid mistakes.
Pay attention to signs. The signs of the charges determine whether the force is attractive or repulsive. This is a critical factor.
Break it down. When dealing with multiple charges, tackle the problem one pair of charges at a time. Calculate the force between each pair and then find the net force.
Be patient. These problems can get a little tricky, especially when dealing with angles. Take your time, break the problem into smaller steps, and double-check your calculations.
Practice, practice, practice! The more problems you solve, the more comfortable you'll become with the concepts and the calculations. There are plenty of resources online with worked examples and practice problems.

Conclusion: Mastering Electrostatic Force Calculations

There you have it, guys! We have successfully learned how to calculate the electric force. We started with the basics of Coulomb's Law, walked through a step-by-step example. We discussed the significance of attractive and repulsive forces and, finally, provided some useful tips to ensure you excel in your physics journey. Now you're equipped to handle problems with multiple charges and find the net force acting on any given charge in the system. Remember to apply the principles of Coulomb's Law, take it step by step, and don't hesitate to draw a diagram to help visualize the problem. Keep practicing, and you'll become a pro at these problems in no time! Keep exploring the world of physics, and remember that electrostatics is just one piece of the puzzle. There's a whole universe of fascinating concepts waiting to be discovered! Happy calculating!