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 writtenΦE=∫ E. dA =qencl/ϵ0where ϵ0=8.85×10^−12C^2/(N⋅m^2) is the permittivity of vacuum. How should the integral in Gauss's law be evaluated?

Over a closed surface

Explanation:

Gauss's law: It states that the total electric flux passing through the closed surface is equal to times the total charge enclosed within the surface.

Mathematically representation :

Electric flux=

Where q=Total charge enclosed within surface

=Permittivity  of vacuum

Therefore,the integral in Gauss's law should be evaluated over a closed surface.

Circle in the integration mean closed we can say that closed integral.

so here is the information for current research:

-nrel's geothermal analysts, scientists, and engineers perform a full range of research from developing advanced methods of locating and accessing geothermal resources to exploring innovative technologies to extract and produce clean energy from the heat of the earth

and here is the information for the technology of geothermal energy:

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-a geothermal heat pump system consists of a heat pump, an air delivery system (ductwork), and a heat exchanger-a system of pipes buried in the shallow ground near the building

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the total distance that martina travels that day is

(distance from home to mom's office) plus (distance from mom's office to school)

plus (distance from school to library) plus (distance from library to friend's house)

plus (distance from friend's house to martina's house).

(we don't know what any of these distance actually is.)