To understand the meaning of the variables in Gauss’s law, and the conditions under which the law is applicable. Gauss’s law is usually written

ΦE=∫E⃗ ⋅dA⃗ =qenclϵ0ΦE=∫E→⋅dA→=qenclϵ0

, where ϵ0=8.85×10−12C2/(N⋅m2)ϵ0=8.85×10−12C2/(N⋅m2) is the permittivity of vacuum.

How should the integral in Gauss’s law be evaluated?

around the perimeter of a closed loop

over the surface bounded by a closed loop

over a closed surface