 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

2017 resit

For constant $b$, the <curl product rule for a scalar field> gives
$$
\nabla\times[(b\cdot r)b]=\nabla(b\cdot r)\times b=b\times b=0.
$$
Using part (b) and the order of the <cross product>,
$$
\iint_SF\times dS=-\iint_Sn\times F\,dS
=-\iiint_V\nabla\times F\,dV
=\boxed{0.}
$$
Here $dS$ inside a vector product denotes the outward vector area element $n\,dS$. Closedness is the condition that permits replacing the entire surface by the boundary integral of a volume.

Solution

Past exam of the mathematical methods II course of the University of Oxford / 2017 resit / 8 / c / Solution

Past exam of the mathematical methods II course of the University of Oxford / 2017 resit / 8 / c / 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 / 2017 resit / 8 / c / Solution

 Ancestors (12)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)