Calculating Forces on a Charge from Multiple Charges

In summary, two charges -2nC and +2nC are located at (0, 2 m). A third charge, +3 nC, is located at (2 m, 0). Calculate the total force (in vector form) acting on charge +3nC from both +2nC charges.
  • #1
stobbz
13
0

Homework Statement



A charge +2nC is located at (0, 2 m). Another +2 nC charge is
located at (0, -2 m). A third charge, +3 nC, is located at (2 m, 0).
Calculate the total force (in vector form) acting on charge +3nC
from both +2nC charges.

Homework Equations



Coulomb's law in vector form

The Attempt at a Solution



I worked out the force on q3 due to q1 to be:

9.54 nano Newton in the positive x direction and
-9.54 nano Newton in the negative y direction

Next, I worked out the force on q3 due to q2 and got:

9.54 nano Newton in the positive x direction and in the positive y direction.

Adding these together, the component would be zero and the total force would be 19.08 nano Newton in the x direction. This would be my answer. However, the answer given is 9.537 nano Newton in the x direction.

Any help is appreciated!
Thanks
 
Last edited:
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  • #2
What is the difference between "in the x direction" and "in the positive x direction"?:confused:
 
  • #3
gneill said:
What is the difference between "in the x direction" and "in the positive x direction"?:confused:

Nothing, I've changed it to avoid any more confusion :smile:
 
  • #4
stobbz said:

I worked out the force on q3 due to q1 to be:

9.54 nano Newton in the positive x direction and
-9.54 nano Newton in the negative y direction

So, a force in the positive y-direction?

19.08 nano Newton in the x direction. This would be my answer. However, the answer given is 19.08 nano Newton in the positive x direction.
You got the right answer?

Please correct and I'll see if I can help...
 
  • #5
hadoque said:
So, a force in the positive y-direction?


You got the right answer?

Please correct and I'll see if I can help...

Ahh sorry, the given answer is 9.537 nN.
 
  • #6
So it looks like you've mucked up a factor of two somewhere. Can you show your calculations? What value did you use for the distance in Coulomb's law?
 
  • #7
gneill said:
So it looks like you've mucked up a factor of two somewhere. Can you show your calculations? What value did you use for the distance in Coulomb's law?

I used 4 (two squared) for the position vector and root 2/2 for the unit vector. This is for the x component for the force on q3 exerted by q1.
 
  • #8
Let's take the case of q1 and q3. q1 is at (0,2), while q3 is at (2,0). The distance betwixt is:

[tex] \sqrt{(2 - 0)^2 + (0 - 2)^2} = \sqrt{4 + 4} = 2 \sqrt{2}[/tex] (meters)
 
  • #9
r13 = (2, -2), unit vector r = root 2 / 2 in the x direction - root 2 / 2 in the y direction,

F13 = Q1Q3 * unit vector / 4 PI Epsilon nought r^2

(with r = 2)
 
  • #10
Ahh ok, now I see where I was going wrong!

Thanks for walking me through that gneill, massively appreciate it.
 

1. What is force acting on a charge?

Force acting on a charge refers to the physical interaction between an electric charge and an electric or magnetic field. It determines the direction and magnitude of the movement of the charge.

2. How is the force acting on a charge calculated?

The force acting on a charge can be calculated using the equation F = qE, where F is the force, q is the charge, and E is the electric field. This equation is known as Coulomb's law.

3. What factors affect the force acting on a charge?

The force acting on a charge is affected by the magnitude of the charge, the strength of the electric or magnetic field, and the distance between the charge and the field source.

4. How does the direction of the electric field affect the force acting on a charge?

The direction of the electric field determines the direction of the force acting on a charge. The force will be in the same direction as the electric field if the charge is positive, and in the opposite direction if the charge is negative.

5. Can the force acting on a charge be negative?

Yes, the force acting on a charge can be negative if the charge is negative and the electric field is in the same direction. This indicates that the force is acting in the opposite direction of the electric field.

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