Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2007 / Paper 2 / Section A / 4

Table of contents
- a 4
  - Solution a
- b 4
  - Solution b
- c 4
  - Solution c

a

Solution

Taking the negative gradient of the potential energy gives the force

f = (- 6 x, - 6 y, - 2 z) .

b

Solution

The divergence is the sum of the three diagonal partial derivatives:

\nabla \cdot f = - 6 - 6 - 2 = - 14.

c

Solution

Each component depends only on its own coordinate, so all cross partial derivatives vanish. Therefore the curl is

\nabla \times f = 0 .

This also follows from the identity that the curl of a gradient vanishes for a twice continuously differentiable potential energy.

 Ancestors (12)

 View article source

 Discussion (0)

There are no discussions about this article yet.

 Articles by others on the same topic (0)

There are currently no matching articles.

  See all articles in the same topic Create my own version