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Ján Lalinský
Ján Lalinský
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According to Griffiths in chapter 11 , given a source of radiation enclosed by a sphere, the power passing through the sphere is $$ P(r) = \oint \mathbf{S} \cdot d\mathbf{a} = \frac{1}{\mu_0} \oint (\mathbf{E} \times \mathbf{B}) \cdot d\mathbf{a}, $$ and the power radiated is: $$ P_{rad} = \lim_{r\to\infty} P(r). $$ What I don't understand is why $r$ has to go to infinity for the power to be defined? I understand that Griffiths definedefines the radiation as the energy transported to infinity, but isn't the power will be the same at every r?

According to Griffiths in chapter 11 , given a source of radiation enclosed by a sphere, the power passing through the sphere is $$ P(r) = \oint \mathbf{S} \cdot d\mathbf{a} = \frac{1}{\mu_0} \oint (\mathbf{E} \times \mathbf{B}) \cdot d\mathbf{a}, $$ and the power radiated is: $$ P_{rad} = \lim_{r\to\infty} P(r). $$ What I don't understand is why $r$ has to go to infinity for the power to be defined? I understand that Griffiths define the radiation as the energy transported to infinity, but isn't the power will be the same at every r?

According to Griffiths in chapter 11 , given a source of radiation enclosed by a sphere, the power passing through the sphere is $$ P(r) = \oint \mathbf{S} \cdot d\mathbf{a} = \frac{1}{\mu_0} \oint (\mathbf{E} \times \mathbf{B}) \cdot d\mathbf{a}, $$ and the power radiated is: $$ P_{rad} = \lim_{r\to\infty} P(r). $$ What I don't understand is why $r$ has to go to infinity for the power to be defined? I understand that Griffiths defines the radiation as the energy transported to infinity, but isn't the power the same at every r?

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Buzz ♦
Buzz ♦
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Why is radiation power is defienddefined at infinity?

According to Griffiths in chapter 11 , given a source of radiation enclosed by a sphere, the power passing through the sphere is:

$$ P(r) = \oint \boldsymbol{S} \cdot d\boldsymbol{a} = \frac{1}{\mu_0} \oint (\boldsymbol{E} \times \boldsymbol{B}) \cdot d\boldsymbol{a} $$

And $$ P(r) = \oint \mathbf{S} \cdot d\mathbf{a} = \frac{1}{\mu_0} \oint (\mathbf{E} \times \mathbf{B}) \cdot d\mathbf{a}, $$ and the power radiated is:

$$ P_{rad} = \lim_{r\to\infty} P(r) $$

What $$ P_{rad} = \lim_{r\to\infty} P(r). $$ What I don't understand is why r$r$ has to go to infinity for the power to be defined? I understand that Griffiths define the radiation as the energy transported to infinity, but isn't the power will be the same at every r?

Why radiation power is defiend at infinity?

According to Griffiths in chapter 11 , given a source of radiation enclosed by a sphere, the power passing through the sphere is:

$$ P(r) = \oint \boldsymbol{S} \cdot d\boldsymbol{a} = \frac{1}{\mu_0} \oint (\boldsymbol{E} \times \boldsymbol{B}) \cdot d\boldsymbol{a} $$

And the power radiated is:

$$ P_{rad} = \lim_{r\to\infty} P(r) $$

What I don't understand is why r has to go to infinity for the power to be defined? I understand that Griffiths define the radiation as the energy transported to infinity, but isn't the power will be the same at every r?

Why is radiation power defined at infinity?

According to Griffiths in chapter 11 , given a source of radiation enclosed by a sphere, the power passing through the sphere is $$ P(r) = \oint \mathbf{S} \cdot d\mathbf{a} = \frac{1}{\mu_0} \oint (\mathbf{E} \times \mathbf{B}) \cdot d\mathbf{a}, $$ and the power radiated is: $$ P_{rad} = \lim_{r\to\infty} P(r). $$ What I don't understand is why $r$ has to go to infinity for the power to be defined? I understand that Griffiths define the radiation as the energy transported to infinity, but isn't the power will be the same at every r?

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EB97
EB97
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Why radiation power is defiend at infinity?

According to Griffiths in chapter 11 , given a source of radiation enclosed by a sphere, the power passing through the sphere is:

$$ P(r) = \oint \boldsymbol{S} \cdot d\boldsymbol{a} = \frac{1}{\mu_0} \oint (\boldsymbol{E} \times \boldsymbol{B}) \cdot d\boldsymbol{a} $$

And the power radiated is:

$$ P_{rad} = \lim_{r\to\infty} P(r) $$

What I don't understand is why r has to go to infinity for the power to be defined? I understand that Griffiths define the radiation as the energy transported to infinity, but isn't the power will be the same at every r?