[Electric Charge Force] I swear I'm doing this right.

In summary, the figure shows seven charged particles with radial distances of d = 1.0 cm or 2d from particle 7, with charges q1 = +8e, q2 = +8e, q3 = +e, q4 = +8e, q5 = +8e, q6 = +4e, and q7 = +4e, where e = 1.60 x 10^-19 C. The net electrostatic force on particle 7 is calculated by finding the x and y components of the force and using the Pythagorean theorem to find the magnitude. The correct magnitude is [436(k^2)(e^4)/(10^-8)]^.5, which
  • #1
Gr33nMachine
12
0

Homework Statement


In the figure below, six charged particles surround particle 7 at radial distances of either d = 1.0 cm or 2d, as drawn. The charges are q1 = +8e, q2 = +8e, q3 = +e, q4 = +8e, q5 = +8e, q6 = +4e, q7 = +4e, with e = 1.60 10-19 C. What is the magnitude of the net electrostatic force on particle 7?---2----
---|-----
1-7-3-4
---|-----
---5----
---|-----
---6----

Homework Equations



F = k(q1)(q2)/(r^2)
k = 8.99e9

The Attempt at a Solution



I split this up into x and y components, and then figured out the sum.

For the x, ƩF = |k(q7*q1)/(r^2) - k(q7*q3)/(r^2) - k(q7*q4)/(4(r^2))|
This simplifies to: |[k(q7)/(r^2)]*[q1-q3-q4/4]|
and so ƩF = |[4ke/(.01^2)]*e(8-1-8/4)| = 4ke/.0001*5e = 20k(e^2)/.0001

I used the same process for the y component. 2 and 5 cancel out since they have the same distance and charge, so the only charge I needed to calculate was for 6. F = k(q7)(q6)/(4(r^2))
This simplifies.. F = k(6e)(4e)/((4)(.0001)) = 6k(e^2)/.0001

Now I just have to add both components for the net charge...

Fx+Fy = 26k(e^2)/.0001 = 5.983744e-23 C

But it's wrong. And the weird thing is, when I calculate the charges seperately, I get slightly different values - to different to be a simple rounding error.
 
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  • #2
You added the components together, how is that magnitude?
 
  • #3
1MileCrash said:
You added the components together, how is that magnitude?

D'oh. Pythagorean Theorom then?

edit: so, ([20k(e^2)/.0001]^2 + [6k(e^2)/.0001]^2)^.5 then?
 
  • #4
Yes, you found the x and y components of the net force vector. The magnitude of that vector, is what you want. You can't add those coefficients of the unit vectors- they aren't like terms.
 
  • #5
Ok, so I got [436(k^2)(e^4)/(10^-8)]^.5 which comes out to 4.8055e-23. This is still incorrect...
 

1. What is electric charge force?

Electric charge force is a fundamental force in nature that is responsible for the interactions between particles that have an electric charge. It is a force that acts between two charged particles, either attracting or repelling them depending on their charges.

2. How is electric charge force calculated?

The electric charge force can be calculated using Coulomb's law, which states that the force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.

3. What are the properties of electric charge force?

Electric charge force has two main properties: it is a conservative force, meaning that the work done by the force is independent of the path taken, and it follows the inverse square law, meaning that the force decreases as the distance between two charged particles increases.

4. How does electric charge force affect matter?

Electric charge force is responsible for the structure and behavior of matter. It is the force that holds atoms and molecules together, and it also plays a role in the behavior of larger objects, such as the movement of electrons in a circuit.

5. How is electric charge force related to other fundamental forces?

Electric charge force is one of the four fundamental forces in nature, along with gravity, strong nuclear force, and weak nuclear force. It is related to the other forces through the theory of electromagnetism, which explains the interactions between charged particles and electromagnetic fields.

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