- #1
patric44
- 303
- 39
- Homework Statement
- find B given the vector potential A
- Relevant Equations
- A = /hat(ρ)/ρ *φ(z,t)
hi guys
this seems like a simple problem but i am stuck reaching the final form as requested , the question is
given the magnetic vector potential
$$\vec{A} = \frac{\hat{\rho}}{\rho}\beta e^{[-kz+\frac{i\omega}{c}(nz-ct)]}$$
prove that
$$B = (n/c + ik/\omega)(\hat{z}×\vec{E})$$
simple enough i found the curl of A which came out to be :
$$B = \frac{\hat{\phi}}{\rho} \beta e^{-iwt} (-k+\frac{i\omega n}{c})e^{-kz+\frac{i\omega n z}{c}}$$
how do i reach the given form of B ?!
this seems like a simple problem but i am stuck reaching the final form as requested , the question is
given the magnetic vector potential
$$\vec{A} = \frac{\hat{\rho}}{\rho}\beta e^{[-kz+\frac{i\omega}{c}(nz-ct)]}$$
prove that
$$B = (n/c + ik/\omega)(\hat{z}×\vec{E})$$
simple enough i found the curl of A which came out to be :
$$B = \frac{\hat{\phi}}{\rho} \beta e^{-iwt} (-k+\frac{i\omega n}{c})e^{-kz+\frac{i\omega n z}{c}}$$
how do i reach the given form of B ?!