Question
An electromagnetic wave of frequency $$1 \times {10^{14}}hertz$$ is propagating along $$z$$-axis. The amplitude of electric field is $$4\,V/m.$$ If $${\varepsilon _0} = 8.8 \times {10^{ - 12}}{C^2}/N - {m^2},$$ then average energy density of electric field will be :
A.
$$35.2 \times {10^{ - 10}}J/{m^3}$$
B.
$$35.2 \times {10^{ - 11}}J/{m^3}$$
C.
$$35.2 \times {10^{ - 12}}J/{m^3}$$
D.
$$35.2 \times {10^{ - 13}}J/{m^3}$$
Answer :
$$35.2 \times {10^{ - 12}}J/{m^3}$$
Solution :
Given:
Amplitude of electric field,
$${E_0} = 4\,v/m$$
Absolute permitivity,
$${\varepsilon _0} = 8.8 \times {10^{ - 12}}{c^2}/N - {m^2}$$
Average energy density $${u_E} = ?$$
Applying formula,
Average energy density $${u_E} = \frac{1}{4}{\varepsilon _0}{E^2}$$
$$ \Rightarrow {u_E} = \frac{1}{4} \times 8.8 \times {10^{ - 12}} \times {\left( 4 \right)^2} = 35.2 \times {10^{ - 12}}J/{m^3}$$