Line, Surface And Volume Integrals - Field Theory.
- The Line integral of Vector A along a path L is given as ∫ L A .dl - The line integral is the dot product of a vector with a specified curve C. - We can also say that line integral is the integral of the tangential component of vector A along the curve C. - If the path of integration is a closed path, the line integral becomes a closed line integral and is called the circulation of A around C. - Line Integral is useful in finding the electric field intensity along a path L. - The surface integral of a vector B across a surface S is defined as ∫ s B .ds - When the surface S is closed, the surface integral becomes the net outward flux of B across S, i.e. - Surface integral is useful in finding the magnetic flux through a surface S. - The volume integral of a scalar T over a volume v is given as ∫ v T . dv SOLVED EXAMPLES/NUMERICALS: Q.1 Calculate the circulation of A = ρ cosφ a ρ + z sinφ a z around the edge L of the wedge defin...