Question

Two positive charges q are located along the y axis at y = +a and y = -a, respectively. (a) What is the electric field at a distance x along the x axis? (b) What does this become for x >> a? (c) For x << a?

Answer 1

a)

In triangle BOC

Using Pythagorean theorem

r = sqrt(a² + x²)

also, Cos = x/r = x/sqrt(a² + x²)

Electric field by each charge is given as

E = kq/r²

E = k q/(a² + x²)

Net electric field is given as

E_net = 2 E Cos

E_net = 2 (k q/(a² + x²)) (x/sqrt(a² + x²))

E_net = 2 kqx / (a² + x²)^3/2

b)

for x>>a

E_net = 2 kqx / x³

E_net = 2 kq / x²

c)

for x <<a

E_net = 2 kqx / a³