# Finding magnitude and direction of an electric field

1. Mar 6, 2017

### fishturtle1

1. The problem statement, all variables and given/known data
A spaceship encounters a single plane of charged particles, with the charge per unit area equal to σ. The electric field a short distance above the plane has magnitude _____ and is directed _____ to the plane.

a) σ/2∈0, parallel

b) σ/2∈0, perpendicular

c) σ/∈0, parallel

d) σ/∈0, perpendicular

e) 2σ/∈0, parallel

2. Relevant equations
E = k * (q/r2)

Electric flux = EAcos(φ)

Electric flux = qenclosed / ∈0

3. The attempt at a solution
I'm given σ = q/A

then q = σA

So i plug this into the electric field equation:

E = kσA/r2

substitute k = 1/4π∈0

E = σA/4πr20

I can make a gaussian surface as a sphere, who's surface area is 4πr2 and then substitute that in for A,

then E = σ/∈0

Now i'm not sure how to find the direction and also i'm unsure how to think about this problem. Is the plane under the spaceship or directly in front of it, and what orientation is it at? Am i supposed to find this?

2. Mar 6, 2017

### haruspex

A short fat cylinder (pillbox) would be more usual here, but the result is the same.
You do need to think about whether all of the flux coming out of it is directed towards the spacecraft, though.
It doesn't matter. The question asks for the orientation of the field in relation to that of the plane (not "spaceplane").