## Electric Flux

• ### Units and Variables

• #### Definition of Electric Flux

${\Phi }_{E}=EA\mathrm{cos}\left(\theta \right)$
• #### Gauss's Law

${\Phi }_{E}=\oint E\cdot \mathrm{dA}=\frac{{q}_{\mathrm{inside}}}{{\epsilon }_{0}}$
• #### Electric Field due to a Point Charge

$E={k}_{e}\frac{q}{{r}^{2}}$
• #### A Spherically Symmetric Charge Distribution (for r > R)

$E={k}_{e}\frac{Q}{{r}^{2}}$
• #### A Spherically Symmetric Charge Distribution (for r < R)

$E={k}_{e}\frac{Qr}{{R}^{3}}$
• #### Electric Field due to a Thin Spherical Shell (for r > R)

$E={k}_{e}\frac{Q}{{r}^{2}}$
• #### Electric Field due to a Thin Spherical Shell (for r < R)

$E=0$
• #### Electric Field due to a Line Charge of Infinite Length

$E=2{k}_{e}\frac{\lambda }{r}$
• #### Electric Field due to a Charged Plane

$E=\frac{\sigma }{2{\epsilon }_{0}}$
• #### Electric Field due to a Conductor (on Surface)

$E=\frac{\sigma }{{\epsilon }_{0}}$
• #### Electric Field due to a Conductor (inside)

$E=0$