Given a vector field $$\overrightarrow F ,$$ the divergence theorem states that

The magnetic vector potential in a region is defined by $$\overrightarrow A = {e^{ - y}}\sin \left( x \right){\widehat a_z}.$$ An infinitely long conductor, having a cross section area, $$a=5$$ $$m{m^2}$$ and carrying a $$dc$$ current, $${\rm I} = 5\,A$$ in the $$Y$$ direction, passes through this region as shown in Fig. Determine the expression for $$(a)$$ $$\overrightarrow B $$ and $$(b)$$ force density $$\overrightarrow f $$ exerted on the conductor

The determinant of the matrix $$\left[ {\matrix{ 1 & 0 & 0 & 0 \cr {100} & 1 & 0 & 0 \cr {100} & {200} & 1 & 0 \cr {100} & {200} & {300} & 1 \cr } } \right]$$ is

Given a vector field $${\overrightarrow F ,}$$ the divergence theorem states that