Electric field of discrete point charges

In summary: R = radius of circleIn summary, the conversation discusses the placement of five equal negative point charges around a circle and how to calculate the electric field at the center of the circle. The correct calculation for the electric field is -kq/R^2, as confirmed by the book. The conversation also addresses a misconception about using symmetry arguments in the calculation.
  • #1
mborn
30
0
Five equal negative point charges (-q) are placed symmetrically around a circle of radius R. Calculate the electric field at the center of the circle.

My Answer:

Each one will be place 72 degrees from the other one (360/5),
Each field line is directed toward the center (charges are negative),
I had;

E_x = (kq/R^2)[-cos 72 + cos 36 + cos 36 - cos 72]
= kq/R^2

E_y = (kq/R^2)[- sin 72 - sin 36 + sin 36 - sin 72]
= 0 N/C

My book says that both E_x and E_y are zero, What did I do that was wrong?

mbron
 
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  • #2
why do you only have 4 charges in your calculations? plus, i don't think you are calculating the distance squared properly, think about it some more

anyways, i would just make a symmetry argument. hey, works for MIT
 
  • #3
Remember that the distance between the centre and any point is R. However, the distance in the x and y direction is not R.
 
  • #4
DarkEternal,
Thanks! I missed the one on the x-axis. This gives me -kq/R^2 which will cancel the other equal but positive term.

Parth Dave,
x- and y- have nothing to do with the problem as I am asked to find E at the center. Thank you for caring to answer me.

mborn
 
Last edited:

1. What is an electric field of discrete point charges?

The electric field of discrete point charges is a physical concept that describes the influence of electric charges on each other. It is a vector field that represents the direction and strength of the electric force that would be experienced by a test charge placed at a given point in space.

2. How is the electric field of discrete point charges calculated?

The electric field of discrete point charges can be calculated using Coulomb's Law, which states that the force between two point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. The electric field is then determined by dividing this force by the magnitude of the test charge.

3. Can the direction of the electric field of discrete point charges be negative?

Yes, the direction of the electric field can be negative. The direction of the electric field is determined by the direction of the force that would be experienced by a positive test charge. If the force would be in the opposite direction of the electric field, then the direction is considered negative.

4. How does the electric field of discrete point charges affect charges placed within it?

The electric field of discrete point charges exerts a force on any charge placed within it. If the charge is positive, it will experience a force in the direction of the electric field, and if it is negative, it will experience a force in the opposite direction. The strength of the force depends on the magnitude of the charge and the strength of the electric field at that point.

5. Can the electric field of discrete point charges be shielded?

Yes, the electric field of discrete point charges can be shielded. This can be done by placing a conductive material between the point charges and the test charge. The conductive material will redistribute the electric field, reducing its strength at the point where the test charge is placed.

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