4 Charges at the corners of a square

In summary, the problem involves finding the magnitude of the electric field at the center of a square with charges placed at the corners (+4 uC at (0,0), +4 uC at (1,1), +3 uC at (1,0), and -3 uC at (0,1)). Using the equation E=k(Q/r^2), the individual field vectors are calculated to be 71934.4 N/C, 53950.8 N/C, 53950.8 N/C, and -53950.8 N/C respectively. The field of the two +4 uC charges cancel out, resulting in a total field of 107900 N/C. The answer is 1.
  • #1
Ortix
64
0

Homework Statement



Consider a square which is 1m on a side. Charges are placed at the corners of the square as follows:

+4 uC at (0,0)
+4 uC at (1,1)
+3 uC at (1,0)
-3 uC at (0,1)

What is the magnitude of the electric field at the square's center?

Homework Equations



E= k(Q/r^2)

(sorry i suck at latex, don't know how to use it)

The Attempt at a Solution



Well I thought this was fairly simple. I just plugged in Q and for r^2 i used cos(45)^2 since the the distance to the center is 1cos(45) = sqrt(2)/2

This gave me 3 different values. for the 4 uC's i got 71934.4 N/C, for the +3 i got 53950.8 and for the -3 i got -53950.8.

So these are the fields in their respective direction. To calculate the magnitude I sum them all, square them and then take the square root. That gives me 143868. However this is not one of the answers:

1.1E5
1.3E5
1.5E5
1.7E5

Anyone have any idea if i did something wrong?
 
Physics news on Phys.org
  • #2
Could you show please the direction of the individual field vectors?

ehild
 
  • #3
[PLAIN]http://img831.imageshack.us/img831/1600/unledss.jpg

I hope this is right

1 2 and 4 are positive whereas 3 is negative
 
Last edited by a moderator:
  • #4
It is right. What can you say about the field of the two 4μC charges? What is the direction of the resultant?

ehild
 
  • #5
Well it should cancel right? Since they are the same magnitude and opposite direction. So would i just sum field's 3 and 2, square them and then take the square root?
 
  • #6
Well, you add only those two fields. You know their magnitudes, don't you? and they point in the same direction, so what is the magnitude of their sum? Why do you square and take the square root?

ehild
 
  • #7
The reason why i square and take the square root is because my book says so :P But i realized that I already know the magnitude and direction (in the book it was calculated separately) so I just need to add them which gives me 107900. Is that correct? Would the answer be 1.1E5?
 
  • #8
Ortix said:
The reason why i square and take the square root is because my book says so :P But i realized that I already know the magnitude and direction (in the book it was calculated separately) so I just need to add them which gives me 107900. Is that correct? Would the answer be 1.1E5?


Yes. :smile:

ehild
 
  • #9
sweet! Thanks man :)
 

FAQ: 4 Charges at the corners of a square

What are the characteristics of a square?

A square is a geometric shape with four equal sides and four equal angles of 90 degrees each. It has two diagonals that bisect each other at 90 degrees and four corners or vertices.

What is the significance of four charges at the corners of a square?

Four charges at the corners of a square represent a system of four point charges placed at the vertices of a square. This configuration is commonly used in physics and chemistry experiments to study the behavior of electric or magnetic fields.

How are the charges arranged in a square configuration?

In a square configuration, the charges are placed at the four corners of the square with equal distance between them. The charges can be of the same magnitude and sign, or they can be different, depending on the experiment being conducted.

What is the net force on a charge at the center of a square due to the four corner charges?

The net force on a charge at the center of a square due to the four corner charges depends on the magnitude and sign of each charge and the distance between them. If the charges are of the same magnitude and sign, the net force will be zero. If the charges are different, the net force will be non-zero and will depend on the distance between the charges.

How does the distance between the charges affect the net force on a charge at the center of a square?

The net force on a charge at the center of a square is directly proportional to the distance between the charges. As the distance between the charges increases, the net force decreases, and vice versa. This relationship is described by Coulomb's law, which states that the force between two charges is inversely proportional to the square of the distance between them.

Similar threads

Electric field created by point charges
Replies
6
Views
334
Electromagnetic force on particles forming a square
Replies
5
Views
2K
Pressure versus stress in uniformly charged sphere
Replies
11
Views
555
E&M: Forces resulting from Charges at the Corners of a Cube
Replies
13
Views
1K
Calculating Forces on a Corner with Identical Charges
Replies
24
Views
2K
Electric charges at the corners of a square
Replies
2
Views
1K
Electric Potential slowing a charged particle to a stop
Replies
4
Views
2K
What is the charge in the middle of the square?
Replies
12
Views
6K
Electric field at a point inside a non-uniformly charged sphere
Replies
6
Views
741
Motion of 4 charges positioned in a square shape
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top