I'm struggling with a problem concerning cross products. I have a perturbation to a background magnetic field given by

$\delta E \times B$

where $B(r(\phi),\phi)= \frac{B_0R_E^3}{r(\phi)^3} + \Delta B(r)\cos\phi$, so $r$ is a polar curve in terms of $\phi$. I was wondering how to go about the cross product? I assume that

$\delta E = \delta E_r \hat{r} + \delta E_\phi \hat{\phi}$

but how can I decompose the functional form of B into its vector form to complete the cross product?

EDIT Am I correct in this approach?:

$\vec{B} = (r(\phi),\phi,B(r,\phi))$

\begin{vmatrix} \hat{r} & \hat{\phi} &\hat{z} \\ \delta E_r & \delta E_\phi & 0 \\ r & \phi & B \end{vmatrix}

where the zero is present because I am considering B which has no height component


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.