- #1

Kaguro

- 221

- 57

- Homework Statement
- Given that total power emitted by a source is P. Find the electric field strength at a distance r from the spherically symmetric source.

- Relevant Equations
- $$\vec S=\frac{1}{\mu_0} \vec E \times \vec B$$

$$c=\frac{1}{\sqrt{\mu_0 \epsilon_0}} $$

E=B*c

The Poynting vector $$\vec S=\frac{1}{\mu_0} \vec E \times \vec B$$ gives the power per unit area. If I need this in terms of electric field only,I should be able to write B=E/c (for EM wave)

Assuming they're perpendicular, ##S =\frac{1}{\mu_0 c}E^2##. Now, ##c=\frac{1}{\sqrt{\mu_0 \epsilon_0}} \Rightarrow c^2 \epsilon_0 = \frac{1}{\mu_0}##

So, ##S =c \epsilon_0 E^2##

I am given the total power emitted as P. I need to find E at distance r. So, ##P= 4 \pi r^2 S##. And so I find,

$$\frac{P}{4 \pi r^2}= c \epsilon_0 E^2$$

But in the book the Poynting vector is given as: ##S =\frac{c \epsilon_0 E^2}{2}##

So... I need to assume that magnetic field contributes to the total power separately, and when asked for electric field, I should not convert EB as E^2/c ?

Assuming they're perpendicular, ##S =\frac{1}{\mu_0 c}E^2##. Now, ##c=\frac{1}{\sqrt{\mu_0 \epsilon_0}} \Rightarrow c^2 \epsilon_0 = \frac{1}{\mu_0}##

So, ##S =c \epsilon_0 E^2##

I am given the total power emitted as P. I need to find E at distance r. So, ##P= 4 \pi r^2 S##. And so I find,

$$\frac{P}{4 \pi r^2}= c \epsilon_0 E^2$$

But in the book the Poynting vector is given as: ##S =\frac{c \epsilon_0 E^2}{2}##

So... I need to assume that magnetic field contributes to the total power separately, and when asked for electric field, I should not convert EB as E^2/c ?