Question

9. State the divergence theorem. Describe the regions over which the integrations are carried out and the quantities that are being integrated. Consider the vector field 22 V = i ++2k V. V =- i+yj + zk Write the equations of limiting surfaces and their normals of the volume defined by its vertices (1,0,0), (0, 1,0), (-1,0,0) and (0,0,1) which define a triangular pyramid. Calculate the value of the divergence of V for this volume. Use the divergence theorem to verify the result.

Answer 1

Gauss Divergence Theorem If F is differentiable vector function in bounded by the closed surface s continuously the region then E IS FONAS = SFF dva 10 where N is out word unit normal vector voi + gj + 2k VVS (K) + (y) + (2) = x +1+1 = 2+1 - SS S klang de dy dz 20 Y=0 x=-1 250 Yzo 20 go dy dz es [2 + 2) - (-2+7)] dy dz - " S s dy dz - 4 oz 220 g zo zo - ų oll a