 Home

Codex Wiki

List of universities

University of Oxford

Course of the University of Oxford

Undergraduate course of the University of Oxford

Physics course of the University of Oxford

Year 1 of the physics course of the University of Oxford

Mathematical methods II course of the University of Oxford

Past exam of the mathematical methods II course of the University of Oxford

2013

On the <punctured plane> $x^2+y^2>0$, write $M=-y/(x^2+y^2)$, $N=x/(x^2+y^2)$. Direct differentiation gives
$$
N_x=\frac{y^2-x^2}{(x^2+y^2)^2}=M_y.
$$
There is no $z$ dependence or $z$ component, so
$$
\boxed{\nabla\times\mathbf F=(0,0,N_x-M_y)=0\qquad(x,y)\ne(0,0).}
$$
The origin is excluded: the field is undefined there. A zero classical curl away from the origin does not state that the field is smooth on an entire disk containing it.

Solution

Past exam of the mathematical methods II course of the University of Oxford / 2013 / 9 / b / Solution

Past exam of the mathematical methods II course of the University of Oxford / 2013 / 9 / b / Solution

 Ancestors (12)

 Discussion (0)

 Articles by others on the same topic (0)

Past exam of the mathematical methods II course of the University of Oxford / 2013 / 9 / b / Solution

 Ancestors (12)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)