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The area integral of the electric field over any closed surface is equal to the net charge enclosed in the surface divided by the permittivity of space. Gauss’ law is a form of one of Maxwell’s equations, the four fundamental equations for electricity and magnetism.

## What is meant by surface integral?

In mathematics, a surface integral is **a definite integral taken over a surface** (which may be a curve set in space). Just as a line integral allows one to integrate over an arbitrary curve (of one dimension), a surface integral can be thought of as a double integral integrating over a two-dimensional surface.

## What does line integral and surface integral mean?

A line integral is **an integral where the function to be integrated is evaluated along a curve** and a surface integral is a generalization of multiple integrals to integration over surfaces. It can be thought of as the double integral analog of the line integral. … We will begin with real-valued functions of two variables.

## What is the difference between surface area and surface integral?

Edit: **The surface integral of the constant function 1 over a surface S equals the surface area of S**. In other words, surface area is just a special case of surface integrals. A similar thing happens for line integrals: the line integral of the constant function 1 over a curve equals the length of the curve.

## Can a surface integral be negative?

So the dot product →v⋅d→S gives the amount of flow at each little “patch” of the surface, and can be positive, zero, or **negative**. The integral ∫→v⋅d→S carried out over the entire surface will give the net flow through the surface; if that sum is positive (negative), the net flow is “outward” (“inward”).

## What is surface and volume integrals?

29.2. Introduction. A vector or scalar field – including one formed from a vector derivative (div, grad or curl) – can be integrated over a surface or volume. This Section shows how to carry out such operations.

## What does dA mean calculus?

dA is a symbol that is generally used to denote **a surface element**. It can optionally have a direction, which is then perpendicular to the surface element. In e.g. polar coordinates it would be dA=rdθdr. endgroup.

## Can a line integral be zero?

You can interpret the line integral being zero to have some special meaning: … If we now move the object along a given path and the path integral is zero, then **we didn’t need to use** any work to do it, i.e. we didn’t need to work against the force field.

## What is the difference between integral and closed integral?

Closed integration in **∫H dl = N i** refers to taking the integral path so that it starts and ends at the same point. While the open integration in ∫B dA = Φ means you have to take a piece of area and integrate over it.