Some equations with minus signs that I want to remember:

\[V_b - V_a = - \int_a^b \vec{E} \cdot d\vec{l}\]

where \(d\vec{l}\) points along the path you’re taking from \(a\) to \(b\).

At the surface of a conductor:

\[\vec{E} = \frac{\sigma}{\epsilon_0} \hat{n}\]

Notice the surface charge density \(\sigma\) is positive if the E-field points out of the surface. That makes sense, right? because E-field lines should start on positive charges.

and

\[\sigma = -\epsilon_0 \frac{dV}{d\hat{n}}\]

where \(\vec{n}\) is the vector perpendicular to the surface. Note that you have to get that vector in the correct direction in order to get the correct sign of the charge.

\[\nalba^2 = -\frac{\rho}{\epsilon_0}\]