# Manipulation of Electromagnetic fields using curls clarification

• gedanken6
In summary, the conversation discusses the representation of a general electromagnetic plane wave using complex exponentials and the application of Faraday's Law to this representation. The conversation also touches on the use of curl in spherical polars and the dot product in representing k and r. Ultimately, it is suggested to start with Faraday's Law and use Stokes' theorem to show the validity of the given relationship between E0 and B0.
gedanken6

## Homework Statement

Question 1. General Plane Waves.
We may represent a general electromagnetic plane wave by (real part of the complex exponentials)
$E=E_{0}*e^(i*k*r-iwt) B=B_{0}*e^(i*k*r-iwt)$

Show that Faraday's Law becomes iwB0=-ik x Eo

## Homework Equations

dB/dt=- curl of E

## The Attempt at a Solution

I transformed dB/dt into iwB0e^(ikr-iwt).

Attempted to perform curl of E on Eoe^(ikr-iwt) but not sure how to work with the r. I thought you might use curl in spherical polars but then you have theta and phi components and I think there's only x, y and z

hi gedanken6!
gedanken6 said:
$E=E_{0}*e^(i*k*r-iwt) B=B_{0}*e^(i*k*r-iwt)$

… not sure how to work with the r. I thought you might use curl in spherical polars …

just because there's an r, that doesn't mean it stands for "radius"!

k*r simply means kxi + kyj + kzk

(erm … different k)

No, it's the dot product:
$$\vec{k}\cdot \vec{r}=k_x x+k_y y+k_z z.$$

1 person
oops!

thanks, vanhees71!

Start with faraday's law, use Stokes' theorem to produce Maxwell's law for del x E, then just use the given plane wave equations to show the validity of the given relationship between E0 and B0, which is just a matter of some differential calculus.

## 1. How can electromagnetic fields be manipulated using curls?

Electromagnetic fields can be manipulated using curls through the use of specialized equipment such as antennas, coils, and conductors. These devices create magnetic fields that can be controlled and directed to produce desired effects.

## 2. What is the purpose of manipulating electromagnetic fields using curls?

The purpose of manipulating electromagnetic fields using curls is to harness and control the energy of these fields for various applications. This can include wireless communication, power transmission, and medical treatments.

## 3. What are some common techniques for manipulating electromagnetic fields using curls?

Common techniques for manipulating electromagnetic fields using curls include induction, resonance, and phased array systems. These methods involve manipulating the strength, direction, and frequency of the electromagnetic fields.

## 4. What are some potential benefits of manipulating electromagnetic fields using curls?

The potential benefits of manipulating electromagnetic fields using curls include improved efficiency in wireless communication, increased range and power in power transmission, and more precise and targeted medical treatments.

## 5. Are there any potential risks or drawbacks to manipulating electromagnetic fields using curls?

Like any technology, there are potential risks and drawbacks to manipulating electromagnetic fields using curls. These can include interference with other electronic devices, health concerns related to exposure to electromagnetic fields, and the need for careful regulation and control to prevent misuse.

Replies
1
Views
1K
Replies
2
Views
2K
Replies
1
Views
2K
Replies
3
Views
1K
Replies
18
Views
4K
Replies
4
Views
2K
Replies
3
Views
415
Replies
1
Views
758
Replies
2
Views
5K
Replies
2
Views
2K