Question

Vector Fields A vector field has a more complicated derivative, because as you go from point to point in the field, you find that not only the magnitude of the vector can be changing, but also its direction Think of a vector field v(..); for instance, the flow velocity of a turbulent gas through some part of space. At each point, v has a certain magnitude and direction. Alternatively, we can split v up into its three components, Vy. Vy and V, at each point. Doing this, we see that a vector field is really made up of three scalar fields vx(X2), vv(x) and V (). a ova We can differentiate each of these components with respect to either x, y or z, so there are nine possible partial derivatives altogether, at each point (XX.). Put these into a table: The most convenient way to define the derivatives of a vector field is to make use of the mathematical shorthand notation called the del operator: Vaig tjener I use x "Yz interchageably 212121 |*| 81**|3| To make sense, V has to be applied to something (just as dar doesn't mean anything by itself). We define:

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Answer 1

Son given a field z direction) 2 v=a (along For care aso, figure ? For case aco, figure 2. V.Talithjen from the figure 1. ақ 8 - da @ SO dz w rix ♡ T.5 =0 alwayn Zero. figure 3. figure 2. Viū N. figure 3,