Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

In a wave guide, graphics of propagation of Transversal Magnetic modes show closed field lines for the electric field.

For example, for a rectangular guide:

$E_x (x,y,z) = \frac {-j\beta m \pi}{a k^2_c} B_{mn}\cos\frac{m\pi x}{a}\sin\frac{n\pi y}{b}e^{-j(\beta z + \omega t)}$

$E_y (x,y,z) = \frac {-j\beta n \pi}{b k^2_c} B_{mn}\sin\frac{m\pi x}{a}\cos\frac{n\pi y}{b}e^{-j(\beta z + \omega t)}$

$E_z (x,y,z) = B_{mn}\sin \frac{m\pi x}{a}\sin\frac{n\pi y}{b}e^{-j(\beta z + \omega t)}$

Is it possible to have closed lines for the electric field?

share|improve this question

1 Answer 1

Yes, it is possible. Maxwell's equations say $$ \oint_l \vec{E}\; d\vec{l} = -\frac{1}{c}\int_{S(l)}\frac{\partial \vec{B}}{\partial t} d\vec{S}. $$ The electric field of this closed line is proportional to the rate of the change of the magnetic flux.

There is no problem with energy conservation. An electron moving along this closed line will be accelerated but it consumes the energy we waste to keep the field changing. This effect is used in some particle accelerators while the reversal effect is used in most microwave sources where the EMW consumes the kinetic energy of moving electrons.

share|improve this answer
1  
In fact this is how electrical transformers work. @Maksim you might want to add that to your answer... –  FrankH Jan 25 '12 at 20:52

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.