![]() ![]() (6.3.4) (6.3.4) C l o s e d S u r f a c e q e n c 0. The formula to calculate the mass of a thin wire lying along a curve C with density S(x, y, z) is given by the line integral: ∮(S ds), where ds is the differential arc length along the curve. According to Gauss’s law, the flux of the electric field E E through any closed surface, also called a Gaussian surface, is equal to the net charge enclosed (qenc) ( q e n c) divided by the permittivity of free space (0) ( 0): ClosedSurface qenc 0. dr), where dr is the differential displacement vector along the curve.ġ1.To calculate the work done by a vector field (force field F) moving an object along a curve C, you can use the line integral: ∮(F To sketch vector fields, calculate divF (divergence), and curIF (curl), you can use graphical methods or computational tools.ġ0. To find the potential, we need to find a scalar function φ such that F = ∇φ. A conservative vector field is a field F with the property that the line integral of F along any closed curve is zero. ![]() The formula for the area of the surface z = f(x, y) is given by the double integral: ∬√(1 + (∂f/∂x)² + (∂f/∂y)²) dA.
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