Calculating Electrostatic Force with Coulomb's Law

In summary: So close! I'm sorry I didn't see it in your work; I should have.In summary, the net electrostatic force acting on the 100 microC charge in a 3.0m X 4.0m rectangle with fixed point-charges at the corners (q1 = 100 microC (0, 4m), q2 = 36 microC (4m, 3m), q3 = 125 microC (0, 3m), and q4 = 32 microC (0,0)) can be calculated using Coulomb's Law and the angle of 53.13 degrees (calculated using a 3-4-5 triangle).
  • #1
antiderivativ
17
0
Four point-charges are fixed at the corners of a 3.0m X 4.0m rectangle. The coordinates of the corners and the values of the charges are listed below.
q1 = 100 microC (0, 4m), q2 = 36 microC (4m, 3m), q3 = 125 microC (0, 3m) and q4 = 32 microC (0,0). Compute the net electrostatic force acting on the 100 microC charge.
ke = 8.99 x 109

I'm using Coulomb's Law.
F = [tex]\frac{ke*q1*q2}{r^2}[/tex]

Here is my attempt at a solution. Is it correct?

6-1.jpg
 
Last edited:
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  • #2


Hi antiderivativ,

antiderivativ said:
Four point-charges are fixed at the corners of a 3.0m X 4.0m rectangle. The coordinates of the corners and the values of the charges are listed below.
q1 = 100 microC (0, 4m), q2 = 36 microC (4m, 3m), q3 = 125 microC (0, 3m) and q4 = 32 microC (0,0). Compute the net electrostatic force acting on the 100 microC charge.
ke = 8.99 x 109

I'm using Coulomb's Law.
F = [tex]\frac{ke*q1*q2}{r^2}[/tex]

Here is my attempt at a solution. Is it correct?

6-1.jpg

No, I don't believe that is correct. When you find the components of F13, you are using an angle of 45 degrees. It would have been a 45 degree angle if the charges were at the corners of a square, but since this is a rectangle it will be different.

You can use your 3-4-5 triangle you have on the page to find the correct angle. What do you get?
 
  • #3


Thanks for the reply! My new angle is 53.13. Is this better? :)
6-2.jpg
 
  • #4


antiderivativ said:
Thanks for the reply! My new angle is 53.13. Is this better? :)
6-2.jpg

Really close! But you changed your triangle when you calculated the angle, and that gave you the wrong angle.

If you look at the 3-4-5 triangle about halfway down the page on the left side, the 3 side is vertical and the 4-side is horizontal, and that matches your problem and calculation.

At the bottom of the page, you switched the 3 and 4 sides. You did the correct procedure; it's just that if you use your original triangle, you'll do:

[tex]
\tan^{-1}\left(\frac{3}{4}\right)
[/tex]

instead of the arctangent of 4/3.
 

What is Coulomb's Law?

Coulomb's Law is a fundamental law of electrostatics that describes the force between two electrically charged particles. It states that the force of attraction or repulsion between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

What is the formula for calculating electrostatic force using Coulomb's Law?

The formula for calculating electrostatic force is F = k(q1q2)/r2, where F is the force in Newtons, k is the Coulomb constant (9 x 10^9 Nm2/C2), q1 and q2 are the charges in Coulombs, and r is the distance between the two charges in meters.

What is the unit of measurement for electrostatic force?

The unit of measurement for electrostatic force is Newtons (N). This is the standard unit for force in the International System of Units (SI).

How does the distance between two charged particles affect the electrostatic force?

The distance between two charged particles has an inverse square relationship with the electrostatic force. This means that as the distance between the particles increases, the force decreases, and vice versa.

Can Coulomb's Law be used to calculate the force between multiple charged particles?

Yes, Coulomb's Law can be used to calculate the force between multiple charged particles. In this case, the total force on a particle is the sum of the individual forces between that particle and each of the other particles.

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