# Help with Coulomb's law: Net electrostatic force

• mousey
In summary, you tried calculating the force with Coulomb's law, then calculating the forces for each vector individually and adding, but you got it wrong both ways. We need your solution to find what went wrong.

#### mousey

Homework Statement
Given the arrangement of charged particles in the figure below, find the net electrostatic force on the
q1 = 5.35-µC charged particle. (Assume q2 = 14.33 µC and q3 = −18.12 µC. Express your answer in vector form.)

The three charges (q1, q2, and q3) are located at the following points:
q1: (-2.00cm, 0cm)
q2: (1.00cm, 1.00cm)
q3: (0cm, -1.00cm)

I converted uC into C and cm into m, found the distance between q1 and q2 (r_12) and between q1 and q3 (r_13), and I know I have to compare q2 to q1 and q3 to q1. I can figure out the force just by plugging numbers into Coulomb's law, but I'm not sure how to calculate the vector components.

Thank you!
Relevant Equations
F =(k{q_1}(q_2))\ d^{2)
(Coulomb's Law)
I tried just calculating the force with Coulomb's law, then calculating the forces for each vector individually and adding, but I got it wrong both ways

Delta2
We need your solution to find what went wrong.

Gordianus said:
We need your solution to find what went wrong.
Thank you! I tried uploading a picture of my work but I couldn't figure out how to initially. Also here's the original problem in all it's glory.

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The modulus of F12 Is 690 N/C. However its components are larger than that value. There's something wrong there.

Delta2
Gordianus said:
The modulus of F12 Is 690 N/C. However its components are larger than that value. There's something wrong there.
Right, I tried that answer and it was marked wrong, so I tried finding the force for the individual vector components (table in the lower left), by using just the distance in the x and y directions, but in meters in place of "d" for d^2. Then I added the components (i of q2 + i of q3, j of q2 +j of q3), but that answer was also wrong.

Haven’t checked the details of arriving at F12 and F13, but they look about right. After that I am lost. How did you get those component force values in the table?

Delta2
haruspex said:
Haven’t checked the details of arriving at F12 and F13, but they look about right. After that I am lost. How did you get those component force values in the table?
these are my equations. Basically in terms of a right triangle, I used the "legs" to calculate for each vector component instead of the hypotenuse as the whole force.

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I checked the modulus in a hurry and they look OK. I don't understand the table

Delta2
Gordianus said:
I checked the modulus in a hurry and they look OK. I don't understand the table
I tried to explain it further in my reply to haruspex.

mousey said:
these are my equations. Basically in terms of a right triangle, I used the "legs" to calculate for each vector component instead of the hypotenuse as the whole force.
You have a basic misunderstanding in how to find the components. You should not be dividing by e.g. 0.03^2.

Delta2
Having found the overall force magnitude, multiply it by the cosine of the angle (x/r) to find the i component and sine (y/r) to find the j component.
Watch the signs carefully.

Delta2 and hutchphd
haruspex said:
Having found the overall force magnitude, multiply it by the cosine of the angle (x/r) to find the i component and sine (y/r) to find the j component.
Watch the signs carefully.
That makes perfect sense. Thank you.

berkeman

## 1. What is Coulomb's law?

Coulomb's law is a fundamental law of electrostatics that describes the relationship between the net electrostatic force between two charged particles and the distance between them. It states that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

## 2. How is Coulomb's law used to calculate the net electrostatic force?

To calculate the net electrostatic force between two charged particles, we use the equation F = k(q1q2) / r2, where F is the net force, k is the Coulomb's constant, q1 and q2 are the charges of the particles, and r is the distance between them.

## 3. What is the unit of measurement for the net electrostatic force?

The unit of measurement for the net electrostatic force is Newtons (N) in the SI system or dyne in the CGS system.

## 4. How does the net electrostatic force change with distance?

The net electrostatic force decreases as the distance between two charged particles increases. This is because the force is inversely proportional to the square of the distance between them. As the distance increases, the force decreases exponentially.

## 5. Can Coulomb's law be used to calculate the force between more than two charged particles?

Yes, Coulomb's law can be extended to calculate the net electrostatic force between multiple charged particles. The net force on a specific particle is the vector sum of the individual forces between that particle and all other particles in the system.