Three identical charges q form an equilateral triangle of si

Three identical charges q form an equilateral triangle of side a, with two charges on the x axis and one on the positive y axis. Find an expression for the electric field at points on the y axis above the uppermost charge. Enter your answers numerically separated by a comma. Show that your result reduces to the field of a point charge 3q for y >> a.

Solution

Let y be a point on y axis such that y > a sqroot(3)/2 ( i.e height of the triangle )

Electric field due to one bottom charge on y axis = Kq/a² x cos 30 = kq/ 2a ²

Therefore due to two charges = Kq/a ²

Electric field due to upper most charge = Kq / (y-a)²

So the total Electric field = Kq ( 1/a² + 1/(y-a)² )

Part B

y >>a , point charge 3q , subsitute in the earlier term, you will get

E = 3 kq/ a^{2 ,}