Square Electric Charge Problem

In summary, the magnitude of the net force acting on q1 is (kq1q3)/(r2), and it is in the direction of (−150°, +27°).
  • #1
Cimino54
2
1

Homework Statement


Four charges,
q1 = +145 µC, q2 = +55 µC, q3 = −150 µC, and q4 = +27 µC,
are fixed at the corners of a 4 m by 5 m rectangle, as illustrated in the figure below. What are the magnitude (in N) and the direction (in degrees counterclockwise from the +x-axis) of the net force acting on q1? (Assume the x-axis extends from q1 to the right.)
3-p-023.png


Homework Equations


1. Fe = (kq1q2)/(r2)
2. a2 + b2 = c2
3. Fx = Fsinθ
4. Fy = Fcosθ

The Attempt at a Solution


1. I determined the distance between charges 1/3 & 2/4 using Pythagorean theorem.
2. I solved for the forces between all charges using equation 1. I solved for the forces between 1/2, 3/4, 1/4, 2/3, 1/3, and 2/4.
3. I resolved forces 1/3 and 2/4 into x and y components using equations 3 & 4.
4. I add all x components together and all y components together.
5. I used equation 2 to get the overall magnitude of the x+y components.
 
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  • #2
Hi Cimino54 and welcome to PF. :welcome:

You describe what you did, but you do not show what you got and how that relates to what the problem is asking. For example, what is the relevance of solving for all the possible pairs of forces (step 2 in your attempt at solution)? Before you start calculating stuff, you need to have a strategy. What is your strategy here?
 
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  • #3
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  • #4
OK, there are a lot of numbers in your post that are difficult to interpret. For example, at the very bottom I see two sets of x and y components of forces. Both sets are labeled Fx and Fy. Which forces are these? You need to use subscripts to distinguish where they come from. Start from the equation that you have written as ##\vec{F}_{q1}=\vec{F}_{q2}+\vec{F}_{q3}+\vec{F}_{q4}##. That's a good starting point. Now you need to write the 6 components on the right, namely Fq2x, Fq2y, Fq3x, Fq3y, Fq4x, Fq4y. Can you do that? Also, I see triangles in your solution that have a 45o angle. What angle is that? How is it formed?
 
  • #5
kuruman said:
OK, there are a lot of numbers in your post that are difficult to interpret. For example, at the very bottom I see two sets of x and y components of forces. Both sets are labeled Fx and Fy. Which forces are these? You need to use subscripts to distinguish where they come from. Start from the equation that you have written as ##\vec{F}_{q1}=\vec{F}_{q2}+\vec{F}_{q3}+\vec{F}_{q4}##. That's a good starting point. Now you need to write the 6 components on the right, namely Fq2x, Fq2y, Fq3x, Fq3y, Fq4x, Fq4y. Can you do that? Also, I see triangles in your solution that have a 45o angle. What angle is that? How is it formed?
Might I suggest starting with something simpler?
Cimino, can you calculate the X and Y components of the force q3 exerts on q1? Please show all your working.
 

Related to Square Electric Charge Problem

1. What is a square electric charge problem?

A square electric charge problem is a physics problem that involves calculating the electric field and/or electric potential at various points around a square-shaped distribution of electric charge. It is a common problem in introductory electromagnetism courses.

2. How do you approach solving a square electric charge problem?

To solve a square electric charge problem, you typically start by drawing a diagram of the square charge distribution and labeling the known values, such as the magnitude and location of each charge. Then, you can use Coulomb's Law and the principle of superposition to calculate the electric field or potential at any desired point.

3. What are the key equations used in solving a square electric charge problem?

The main equations used in solving a square electric charge problem are Coulomb's Law, which gives the magnitude of the electric force between two point charges, and the principle of superposition, which states that the total electric field or potential at a point is the sum of the contributions from each individual charge in the system.

4. Are there any simplifying assumptions made in solving a square electric charge problem?

Yes, in most cases, a square electric charge problem assumes that the charges in the square are point charges (meaning they have no physical size) and that the distance between charges is much larger than the size of the square. Additionally, the problem may also assume that the charges are evenly distributed along each side of the square.

5. What are some real-world applications of square electric charge problems?

Square electric charge problems have many real-world applications, including the design of electronic circuits, the behavior of electric fields around square-shaped objects (such as electronic devices), and the calculation of the electric field inside a parallel plate capacitor. They are also used in understanding the behavior of charged particles in accelerators and particle colliders.

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