- Home
- Standard 12
- Physics
8.Electromagnetic waves
hard
The electric field in an electromagnetic wave is given by ${E}=\left(50\, {NC}^{-1}\right) \sin \omega({t}-{x} / {c})$
The energy contained in a cylinder of volume ${V}$ is $5.5 \times 10^{-12} \, {J}$. The value of ${V}$ is $......{cm}^{3}$ $\left(\right.$ given $\left.\in_{0}=8.8 \times 10^{-12} \,{C}^{2} {N}^{-1} {m}^{-2}\right)$
A
$5000$
B
$1500$
C
$500$
D
$100$
(JEE MAIN-2021)
Solution
${E}=50 \sin \left(\omega {t}-\frac{\omega}{{c}} \cdot {x}\right)$
Energy density $=\frac{1}{2} \in_{0} {E}_{0}^{2}$
Energy for volume ${V}=\frac{1}{2} \in_{0} {E}_{0}^{2} \cdot {V}=5.5 \times 10^{-12}$
$\frac{1}{2} 8.8 \times 10^{-12} \times 2500 {V}=5.5 \times 10^{-12}$
${V}=\frac{5.5 \times 2}{2500 \times 8.8}=.0005\, {m}^{3}$
$=.0005 \times 10^{6}\,({c} . {m})^{3}$
$=500({c} \, \cdot {m})^{3}$
Standard 12
Physics
