Question

Write and prove Goss's diversion theorem

Answer 1

Gauss’s Divergence Theorem:

Statement. It states that the volume integral of the divergence of a vector  field A, taken over  any volume, V is equal to the surface integral of A taken over the closed surface surrounding  the volume V and vice versa.

Stoke’s Theorem:

Statement. It states  that the surface integral of curl of a vector field over an open surface equals the line integral of the vector field over the closed curve bounding the surface area and vice versa.

Helmholtz’s Theorem:

Statement. It states that a vector field is completely specified  by itsdivergence and curl or in other words any vector field may be expressed as the sum of an irrotational vector  and a solenoidal vector.