Question

I was studying "line integrals of vector fields" in my Calculus III course. But I don't understand them too well, is there any physical examples of a "line integral of a vector field"? (Can you point out the representation of, the field, the path, and the value of the integral?)

Answer 1

Best and very common Physical example of line integral is workdone by a force field.

Basically , line integral gives the area under curve. To understand this physically , let's take the example of work done by a force .

Work done (w) by a force is given by

  $\int_{a}^{b} F.dx$

Here , we have used line integral of force over the path a to b. And the area under the curve (from a to b ) , represents workdone by this force.

Figure : work done by a force ( very common of line integral )

חד a х