Question

Describe different types of Surface Integral, How are they different from the Flux Integral and why is the Flux Integral so important in the field of engineering?

Answer 1

Generally there are 2 types of surface integrals:-

1. Scalar field surface inegrals 2. Vector field surface integral

1. Let f(r) be measure of some scalar field quantity at a point indicated by position vector r. Then fdsigma is the amount of scalar quantity contained in that bit of surface and the total quantity in the surface is given by double integration of fdsigma.

2. Now let V(r) be any vector field quantity, then the quantity in the small surface is V.ňdsigma is the flux of that quantity, and total flux through the the surface is obtained by double integration of V.ňdsigma.

Flux integral is important in the field of engineering because it is concerned with vector field and most of the practical problem is dealt using flux field , hence it is very critical component in the fieldbof engineering.