I.12.3 Vector Field Circulation

Condition: Calculate the circulation of the vector field \ (\ bar {a} \) through the closed circuit l, which is the intersection of the specified surfaces, directly and according to the stock formula: \ [\ vec {a} = y \ vec {\ iMath} -x \ jmath}+z \ vec {k}, \ quad \ text {l:} \ left \ {\ begin {array} {c} x^{2}+y^{2}+z^{2} = 4 \\\ z^{2} = x^{2}+y^{2} \ end {Array} \ Right. \]