What is wrong with the following calculation? Given the field and curve shown below, we can...

Transcribed Image Text:

What is wrong with the following calculation? "Given the field and curve shown below, we can find the flow of the field across the curve by finding divergence and integrating over the region enclosed by the curve: Out- Out The curve can be given a counter-clockwise parameterization (x[t), ylt]} = (1,0} +(2 Cos[t], 2 Sin[t]}, but that's not important, because we can just look at the divergence of the field: in- divris 1.1 = Together (D(m{x, vl, x) • D{n[x, yl, vll Since it's zero, we don't have to do the integral because the integral of zero is zero and so the flow is zero." What is wrong with the following calculation? "Given the field and curve shown below, we can find the flow of the field across the curve by finding divergence and integrating over the region enclosed by the curve: Out- Out The curve can be given a counter-clockwise parameterization (x[t), ylt]} = (1,0} +(2 Cos[t], 2 Sin[t]}, but that's not important, because we can just look at the divergence of the field: in- divris 1.1 = Together (D(m{x, vl, x) • D{n[x, yl, vll Since it's zero, we don't have to do the integral because the integral of zero is zero and so the flow is zero."