Calculating Net Force on a Point Charge in a 2D Coulomb's Law System

In summary, the problem involves calculating the net force on point charge 1 in a system of point charges. The given information includes the arrangement of the charges, the separation of the charges, and the value of the Coulomb constant. To solve the problem, one must first calculate the forces on charge 1 caused by each of the other charges. These forces can be added together to find the net force on charge 1. The distance between charge 4 and charge 1 can be calculated using trigonometric ratios, and vectors can be added by adding their components.
  • #1
cobhc27
1
0

Homework Statement



Consider the arrangement of point charges shown below. Calculate the net force on point charge 1 given the arrangement of the point charges and the separation of the charges.

1=2=3=e-
2=e+
r=0.4cm
=0.0004m
K=9x10^9
Fnet=?

Please use this link for an image of the "point charges shown below"
http://i277.photobucket.com/albums/kk71/cobhc_27/physics101.jpg

Homework Equations



Fnet=
Kq1q2
r^2


The Attempt at a Solution



Fnet=
Kq1q2
------
r^2

=
kq^2
-----
r^2

I assume you have to solve for 1 2 3 and 4 in this case, but I don't have a great idea on how to. From there, perhaps you add up each net force (but I don't know how to incorporate the 2d part). Any help given is greatly appreciated.
 
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  • #2
cobhc27 said:
From there, perhaps you add up each net force (but I don't know how to incorporate the 2d part

Remember that force is a vector. To add vectors (in two-dimensions or in n-dimensions), add the components of the vector. The components can easily be calculated using trigonometric ratios, especially since you know the angle.

cobhc27 said:
1=2=3=e-
2=e+

Could you clear this up a bit? You have 2 twice.
 
  • #3
It's pretty easy:

1. Calculate the force on 1 caused by 2.
2. Calculate the force on 1 caused by 3.
3. Calculate the force on 1 caused by 4.
4. Add the forces together.

Do you know how to calculate the distance between 4 and 1? Do you know how to add vectors?
 

1. What is Coulomb's Law in 2D?

Coulomb's Law is a fundamental principle in physics that describes the force between two charged particles in a two-dimensional space. It 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.

2. How is Coulomb's Law in 2D different from the 3D version?

The main difference between the two versions is the dimensionality of space. In 3D, the force is inversely proportional to the square of the distance between the two particles, while in 2D, it is inversely proportional to the distance between them. This is because in 2D, the distance between two points is measured as a straight line, while in 3D, it is measured as the shortest distance between the two points, which is a diagonal in 2D.

3. What are the units of measurement for Coulomb's Law in 2D?

The units of measurement for Coulomb's Law in 2D are Newtons (N) for force, Coulombs (C) for charge, and meters (m) for distance. In mathematical terms, it can be represented as Nm^2/C^2.

4. How does the direction of the force between two charged particles in 2D relate to the direction of the distance between them?

The force between two charged particles in 2D is a vector quantity, which means it has both magnitude and direction. The direction of the force is along the line connecting the two particles, and it is attractive if the particles have opposite charges and repulsive if they have the same charge. The direction of the distance between the two particles is also along this line, which means the force and distance have the same direction in 2D.

5. Can Coulomb's Law in 2D be applied to real-life situations?

Yes, Coulomb's Law in 2D is a fundamental principle in physics and is applicable to real-life situations. For example, it can be used to calculate the force between two charged particles in a two-dimensional circuit or the force between positively and negatively charged ions in a two-dimensional crystal lattice.

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