 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

Using $r=(x,y,z)$ and constant $a$, the <divergence> is
$$
\partial_i(\epsilon_{ijk}r_ja_k)=\epsilon_{ijk}\delta_{ij}a_k=0.
$$
For the <curl>, the <curl of a cross product> identity gives
$$
\nabla\times(r\times a)=r(\nabla\cdot a)-a(\nabla\cdot r)+(a\cdot\nabla)r-(r\cdot\nabla)a
=0-3a+a-0.
$$
Thus
$$
\boxed{\nabla\cdot(r\times a)=0,\qquad\nabla\times(r\times a)=-2a.}
$$
For a quick sign check, taking $a=e_z$ gives $r\times a=(y,-x,0)$, whose <curl> is $(0,0,-2)$.

Solution

Past exam of the mathematical methods II course of the University of Oxford / 2017 resit / 3 / b / Solution

Past exam of the mathematical methods II course of the University of Oxford / 2017 resit / 3 / 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 / 2017 resit / 3 / b / Solution

 Ancestors (12)

 Discussion (0)  Subscribe (1)

 Articles by others on the same topic (0)

 Discussion (0)