Question
The $$rms$$ value of the electric field of the light coming from the Sun is $$720\,N/C.$$ The average total energy density of the electromagnetic wave is
A.
$$4.58 \times {10^{ - 6}}J/{m^3}$$
B.
$$6.37 \times {10^{ - 9}}J/{m^3}$$
C.
$$81.35 \times {10^{ - 12}}J/{m^3}$$
D.
$$3.3 \times {10^{ - 3}}J/{m^3}$$
Answer :
$$4.58 \times {10^{ - 6}}J/{m^3}$$
Solution :
$${E_{rms}} = 720$$
The average total energy density
$$\eqalign{
& = \frac{1}{2}{ \in _0}E_0^2 = \frac{1}{2}{ \in _0}{\left[ {\sqrt 2 {E_{rms}}} \right]^2} = { \in _0}E_{rms}^2 \cr
& = 8.85 \times {10^{ - 12}} \times {\left( {720} \right)^2} = 4.58 \times {10^{ - 6}}J/{m^3} \cr} $$