Gauss's Law

Gauss’s law says that the total electric field flowing outward through any closed surface is set entirely by the net charge inside that surface. Charges outside the surface can distort the field at different points on the surface, but their contributions cancel in the total flux. This works because electric field lines begin on positive charge and end on negative charge, so counting how many lines pass through a closed boundary is equivalent to counting the enclosed charge; the constant 1/ε0 converts that charge into the correct field-flux scale.

Use Gauss’s law when a charge distribution has enough symmetry that the electric field is constant over a convenient closed surface, such as spherical, cylindrical, or planar symmetry. It is especially useful for finding electric fields of charged spheres, long wires, infinite sheets, and conducting surfaces.

• Using the total charge in the universe instead of only the charge enclosed by the surface
• Forgetting that Gauss’s law gives total flux, not directly the electric field unless symmetry is used
• Mixing up the sign of Q and therefore the direction of the net flux