# Electric Fields (vectors)

## Homework Statement

The x-y plane contains point charge with magnitudes and positions as follows:

A charge of Q lies at co-ordinates (0, a)
A charge of -Q lies at co-ordinates (0,-a)

Show that the magnitude of the electric field at (b, 0) is given by

E = Qa / [2πε0(a²+b²)^(3/2)]

ε0 = Epsilon nought = 8.85 x10^-12

E = Q/ 4πε0r²

## The Attempt at a Solution

E due to Q is

E1 = Q/ 4πε0r²
E1 = Q/ 4πε0(a²+b²)

Therefore the vector E'

E' = E1*Cos(x) i^ + E1*Sin(x) j^
E' = QCos(x) / 4πε0(a²+b²) i^ + QSin(x)/ 4πε0(a²+b²) j^

E due to -Q is

E2 = Q/ 4πε0r²
E2 = Q/ 4πε0(a²+b²)

Therefore the vector E''

E'' = E2*Cos(x) i^ + E2*Sin(x) j^
E'' = QCos(x) / 4πε0(a²+b²) i^ + QSin(x)/ 4πε0(a²+b²) j^

Vector E = E' + E''
E = QCos(x) / 4πε0(a²+b²) i^ + QSin(x)/ 4πε0(a²+b²) j^
+ QCos(x) / 4πε0(a²+b²) i^ + QSin(x)/ 4πε0(a²+b²) j^
E = QCos(x) / 2πε0(a²+b²) i^ + QSin(x)/ 2πε0(a²+b²) j^

Magnitude of E
E = sqrt{Q²Cos²(x) / [2πε0(a²+b²)]² + Q²Sin²(x)/ [2πε0(a²+b²)]²}

E = Q / 2πε0(a²+b²)

As you can see its close lol, need Q*a not Q by itself and (a²+b²) should be(a²+b²)^(3/2)?