# Rybicki & Lightman, Revised Edition

## Chapter 1. Fundamentals of Radiative Transfer

### Problem 01. Definition of the flux and solid angle

##### Solution

- The direction of the magnetic field of a plane electromagnetic wave.

- The electric field. It is given by

- Property of the electromagnetic waves: The oscillations of electric and magnetic fields are
**perpendicular**to each other, and also**perpendicular**to the direction of energy and wave propagation. - From the electric field , you should find out that the direction of wave propagation is +z direction.

Let’s first consider the fact that two fields are perpendicular to the direction of wave propagation. The possible answers could be (B) and (C).

However, the direction of (C) is parallel to that of the electric field. Thus the choice (C) cannot be an answer.

Therefore, a remaining and the only correct answer is (B).

(B)

- The relation between the triple scalar product and Levi-Civita Symbol

- Vector and scalar product
- Triple scalar product (Problem 1-11)
- Definition of Levi-Civita symbol (Equation 1.67)

- Some properties of Kronecker delta and Levi-Civita Symbol

- Definition of Kronecker delta symbol (Equation 1.14)
- Definition of Levi-Civita symbol (Equation 1.67)

https://en.wikipedia.org/wiki/Kronecker_delta

https://en.wikipedia.org/wiki/Levi-Civita_symbol

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- Angle transformation formulae using vector algebra.

- Basic concept of a vector algebra
- Law of cosines
- Pythagorean trigonometric identity

https://en.wikipedia.org/wiki/Law_of_cosines

https://en.wikipedia.org/wiki/Pythagorean_trigonometric_identity

]]>Thank you, Mateus, for asking this question.

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You can buy the book via

https://www.amazon.com/Radiative-Processes-Astrophysics-George-Rybicki/dp/0471827592

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