Electric field of discrete point charges

[mborn]

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

 

[DarkEternal]

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

 

[Parth Dave]

Remember that the distance between the centre and any point is R. However, the distance in the x and y direction is not R.

 

[mborn]

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