Calculating Force Vectors Between Charged Particles

In summary, the conversation revolved around calculating the force vector F between two charges, Q1 = -2 C and Q2 = 3 C, with a distance of 8.602 mm between them. After discussing the direction of the force vector and determining which force (acting on Q2) to calculate, the magnitude of F was found using Coulomb's law. The components of F were then calculated using the "uniformity" expressions and the final result for F was (5.934*10^-15 N, 4.238*10^-15 N).
  • #1
Mushroom79
26
0

Homework Statement



http://imgur.com/opD71

Q1 = -2 C
Q2 = 3 C

Decide the forcevector F

Homework Equations



F = (k*Q1*Q2)/r^2

k = 8,99*10^9 Nm^2/C^2

The Attempt at a Solution



Q1, Q2 = squarerot(5+7) = 9,24 mm = 0,924 cm = 0,00924 m

F = (8,99*10^9*-2*3)/0,00924 = -5,838 * 10^12 N

Uniformity gives

F/Fx = 0,924/0,7

Fx = F/(0,924/0,7) = -4.423 N

F/Fy = 0,924/0,5

Fy = F/(0,924/0,5) = -3,159 N

F = (-4,423 N, -3,159 N) ?
 
Last edited:
Physics news on Phys.org
  • #2
A few questions for you :
Have you drawn a diagram for this with the direction of the forces on each charge?
What force are you trying to calculate?
What are the positions (or separation) of the 2 charges?
 
  • #3
Mushroom79 said:

Homework Statement



http://imgur.com/opD71
For some reason your image is not showing up, so here's a copy:
attachment.gif

Q1 = -2 C
Q2 = 3 C

Decide the forcevector F
Question: Which force vector do you want? The one acting on Q1 or the one acting on Q2? In other words, F21 or F12?

Homework Equations



F = (k*Q1*Q2)/r^2

k = 8,99*10^9 Nm^2/C^2

The Attempt at a Solution



Q1, Q2 = squarerot(5+7) = 9,24 mm = 0,924 cm = 0,00924
That distance doesn't look right. Better check it.
F = (8,99*10^9*-2*3)/0,00924 = -5,838 * 10^12 N

Uniformity gives

F/Fx = 0,924/0,7

Fx = F/(0,924/0,7) = -4.423 N

F/Fy = 0,924/0,5

Fy = F/(0,924/0,5) = -3,159 N

F = (-4,423 N, -3,159 N) ?
It looks like you're losing a good number of powers of ten from the force. The components should be around the same order of magnitude as the force they add up to; your F (currently) has an order of magnitude of 1012.
 

Attachments

  • Fig1.gif
    Fig1.gif
    1.3 KB · Views: 539
  • #4
Updated picture with direction of the force vector I need (acting on Q2):

http://imgur.com/c7hu8

I'm trying to calculate the vectorforce F

Q1, Q2 = squarerot(5^2+7^2) = 8,602 mm would be the distance between the 2 charges
 
Last edited:
  • #5
You have to decide which force to calculate, the force on Q1 or Q2?
Q2 is the easiest.
Start by working out the magnitude of the force first and then you can do the components.
 
  • #6
Mushroom79 said:
Updated picture with direction of the force vector I need (acting on Q2):

http://imgur.com/c7hu8

I'm trying to calculate the vectorforce F
Vectors have a direction. While the forces acting on the two charges will have the same magnitude, their directions will be opposite -- equal and opposite forces thanks to Newton's third law. So you need to decide which force vector you want to calculate (they differ only in direction).

Here's a picture to make things clear:
attachment.gif

Q1, Q2 = squarerot(5^2+7^2) = 8,602 mm would be the distance between the 2 charges
That looks better.

EDIT: Added diagram.
 

Attachments

  • Fig1.gif
    Fig1.gif
    2.1 KB · Views: 532
Last edited:
  • #7
Okay, let's say I want to calculate the force on Q2.
To get the magnitude (length) isn't it the same as F = squarerot(5^2+7^2) = 8,602 mm ?

After that I use the uniformity F/Fx = F/0,7

F/Fy = F/0,5

Not sure how I know what axis (x or y) should be negative or positive?
 
  • #8
The magnitude of the force is given by Coulomb's law.
F = (k*Q1*Q2)/r^2

You can see the direction of the force vector on gneill's diagram.
If your x-axis is to the right, and your y-axis is straight up, then both components will be positive.
You can use your "uniformity" expressions will a small change :
F/Fx = 8.6/7
F/Fy = 8.6/5

( or you can use trigonometry - it'll come out to the same ).
 
  • #9
ap123 said:
The magnitude of the force is given by Coulomb's law.
F = (k*Q1*Q2)/r^2

You can see the direction of the force vector on gneill's diagram.
If your x-axis is to the right, and your y-axis is straight up, then both components will be positive.
You can use your "uniformity" expressions will a small change :
F/Fx = 8.6/7
F/Fy = 8.6/5

( or you can use trigonometry - it'll come out to the same ).


I see, so:

F = -7,290*10^-14


F/Fx = 8,6/0,7

Fx = (-7,290*10^-14)/(8,6/0,7) = -5,934*10^-15 N

F/Fy = 8,6/0,5

Fy = (-7,290*10^-14)/(8,6/0,5) = -4,238*10^-15 N

F = (5,934*10^-15 N, 4,238*10^-15 N )
 
  • #10
Almost there :)

F = 7.290*10^14 (not -14)
 
  • #11
ap123 said:
Almost there :)

F = 7.290*10^14 (not -14)

Ah, I may be a little too fast sometimes.

Thank you both for great help :smile:
 

Related to Calculating Force Vectors Between Charged Particles

1. What is a force vector?

A force vector is a mathematical representation of a force, which includes both magnitude and direction. It is represented as an arrow, with the length of the arrow representing the magnitude and the direction of the arrow representing the direction of the force.

2. How do you determine the direction of a force vector?

The direction of a force vector is determined by using a coordinate system, such as x-y or polar coordinates. The direction of the vector is measured relative to the positive x-axis in a counterclockwise direction.

3. How do you find the magnitude of a force vector?

The magnitude of a force vector can be found using the Pythagorean theorem. This involves squaring the x and y components of the vector, adding them together, and then taking the square root of the sum.

4. What is the difference between a force vector and a displacement vector?

A force vector represents a physical force acting on an object, while a displacement vector represents the change in position of an object. Both vectors have magnitude and direction, but a force vector is typically used in calculations involving forces, while a displacement vector is used in calculations involving motion.

5. How do you determine the net force acting on an object with multiple force vectors?

To determine the net force acting on an object with multiple force vectors, you must first find the x and y components of each force vector. Then, add all of the x components together and all of the y components together. The resulting x and y components can then be used to find the magnitude and direction of the net force vector.

Similar threads

Calculate electric force using Coulomb's law (vector components are the struggle)
    • Introductory Physics Homework Help
Replies
3
Views
189
Finding the position of a middle charge to have Zero Net Force
    • Introductory Physics Homework Help
Replies
9
Views
1K
How to find distance between 2 charges, with no force given?
    • Introductory Physics Homework Help
Replies
2
Views
1K
Coulomb's Law: Calculating the Force between Two Charged Balls
    • Introductory Physics Homework Help
Replies
4
Views
1K
Net electric force of multiple charged particles in 3-d space
    • Introductory Physics Homework Help
Replies
12
Views
1K
The vector sum of the electric forces exerted on a particle
    • Introductory Physics Homework Help
Replies
3
Views
2K
Electrostatic Force and Field between two charges
    • Introductory Physics Homework Help
Replies
5
Views
1K
Electric field from a charge q1
    • Introductory Physics Homework Help
Replies
10
Views
807
Finding the value of the electric charge
    • Introductory Physics Homework Help
Replies
8
Views
2K
Resolving the electric force into x y components?
    • Introductory Physics Homework Help
Replies
4
Views
1K

Hot Threads

Recent Insights

Back
Top