# Multiplying by unit vector in electric field equation

1. Nov 15, 2009

### ChrisBaker8

1. The problem statement, all variables and given/known data

A 5.0 μC point charge is located at x = 1.0 m, y = 3.0 m, and a −4.0 μC point charge is located
at x = 2.0 m, y = −2.0 m.

a) Find the magnitude and direction of the electric field at x = −3.0 m, y = 1.0 m. [5 Marks]
b) Find the magnitude and direction of the force on a proton at this position in a).

2. Relevant equations

E = (kq/r²) x [r-hat] (couldn't find the symbol for r circumflex)

3. The attempt at a solution

I can work out the first part of the equation, but I'm unsure what r-hat represents and what figure to use. I thought a unit vector was in the form Ai + Bj + Ck, how do you multiply that by a figure to get another single figure?

2. Nov 16, 2009

### rl.bhat

Let point A be ( 1 m, 3 m) and point B be (2 m, -2 m). Let P be the point (-3 m, 1 m) where you want to find the electric field.
First of all find the distances AP and BP. Finding slope of the line AP and BP, you an find the angle made by the electric fields with x-axis. Then resolve them along vertical and horizontal components. Then find ΣEx and ΣEy and E.