# Power lines from an electrically charged ball

1. Nov 6, 2014

### Karol

1. The problem statement, all variables and given/known data
A conductive ball of diameter 0.4 [m] is charged equally with a concentration of $\sigma=8 [micro-coulon/m^2]$.
What's the total number of electric field power lines, N, that extrude from the ball

2. Relevant equations
The electric field near a conductor is like in a capacitor:
$E=\frac{\sigma}{\varepsilon_0}$
Definition of power lines:
$\frac{N}{A}=\varepsilon_0 E$

3. The attempt at a solution
$N=A\cdot \varepsilon_0 \cdot E=\frac{A\cdot\varepsilon_0\cdot\sigma}{\varepsilon_0}=A\cdot \sigma$
$N=4\pi\cdot 0.4[m]^2\cdot 8E-6[Coulon]=1.6E-5[lines]$
It should be N=4E-6[lines]

2. Nov 6, 2014

R = 0.2 m