Question

verify gauss divergence theorem

Answer 1

Example : Verify the divergence theorem for the vector field F + xi " yj " zk over the sphere ' of radius a centred at the origin x" " y" " z" + a". Method 1: Note: the value of the integral ,,,# $dV + volume of region ' + ' & πa#. then *F + %xi " %yj " %zk 1 Page 2 and )*F) + 1 %x!

Answer 2

Verify the divergence theorem if F = xi + yj + zk and S is the surface of the unit cube with opposite vertices (0, 0, 0) and (1, 1, 1). divF dV we calculate each integral separately. The surface integral is calculated in six parts – one for each face of the cube. The total flux through the surface of the cube is 3.