JEE MAIN - Physics (2006 - No. 1)
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
$$4.58 \times {10^{ - 6}}\,J/{m^3}$$
$$6.37 \times {10^{ - 9}}\,J/{m^3}$$
$$81.35 \times {10^{ - 12}}\,J/{m^3}$$
$$3.3 \times {10^{ - 3}}\,J/{m^3}$$
Explanation
$${E_{rms}} = 720$$
The average total energy density
$$ = {1 \over 2}{ \in _0}\,E_0^2 = {1 \over 2}{ \in _0}{\left[ {\sqrt 2 {E_{rms}}} \right]^2} = { \in _0}\,E_{rms}^2$$
$$ = 8.85 \times {10^{ - 12}} \times {\left( {720} \right)^2}$$
$$ = 4.58 \times {10^{ - 6}}\,J/{m^3}$$
The average total energy density
$$ = {1 \over 2}{ \in _0}\,E_0^2 = {1 \over 2}{ \in _0}{\left[ {\sqrt 2 {E_{rms}}} \right]^2} = { \in _0}\,E_{rms}^2$$
$$ = 8.85 \times {10^{ - 12}} \times {\left( {720} \right)^2}$$
$$ = 4.58 \times {10^{ - 6}}\,J/{m^3}$$
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