1
JEE Main 2023 (Online) 11th April Morning Shift
+4
-1

The electric field in an electromagnetic wave is given as

$$\overrightarrow{\mathrm{E}}=20 \sin \omega\left(\mathrm{t}-\frac{x}{\mathrm{c}}\right) \overrightarrow{\mathrm{j}} \mathrm{NC}^{-1}$$

where $$\omega$$ and $$c$$ are angular frequency and velocity of electromagnetic wave respectively. The energy contained in a volume of $$5 \times 10^{-4} \mathrm{~m}^{3}$$ will be

(Given $$\varepsilon_{0}=8.85 \times 10^{-12} \mathrm{C}^{2} / \mathrm{Nm}^{2}$$ )

A

$$17 \cdot 7 \times 10^{-13} \mathrm{~J}$$

B
$$28 \cdot 5 \times 10^{-13} \mathrm{~J}$$
C
$$8 \cdot 85 \times 10^{-13} \mathrm{~J}$$
D
$$88 \cdot 5 \times 10^{-13} \mathrm{~J}$$
2
JEE Main 2023 (Online) 10th April Evening Shift
+4
-1

The amplitude of magnetic field in an electromagnetic wave propagating along y-axis is $$6.0 \times 10^{-7} \mathrm{~T}$$. The maximum value of electric field in the electromagnetic wave is

A
$$6.0 \times 10^{-7} ~\mathrm{Vm}^{-1}$$
B
$$5 \times 10^{14} ~\mathrm{Vm}^{-1}$$
C
$$180 ~\mathrm{Vm}^{-1}$$
D
$$2 \times 10^{15} ~\mathrm{Vm}^{-1}$$
3
JEE Main 2023 (Online) 10th April Morning Shift
+4
-1

The energy of an electromagnetic wave contained in a small volume oscillates with

A
double the frequency of the wave
B
the frequency of the wave
C
half the frequency of the wave
D
zero frequency
4
JEE Main 2023 (Online) 6th April Evening Shift
+4
-1

The energy density associated with electric field $$\vec{E}$$ and magnetic field $$\vec{B}$$ of an electromagnetic wave in free space is given by $$\left(\epsilon_{0}-\right.$$ permittivity of free space, $$\mu_{0}-$$ permeability of free space)

A
$$U_{E}=\frac{\epsilon_{0} E^{2}}{2}, U_{B}=\frac{B^{2}}{2 \mu_{0}}$$
B
$$U_{E}=\frac{E^{2}}{2 \epsilon_{0}}, U_{B}=\frac{\mu_{0} B^{2}}{2}$$
C
$$U_{E}=\frac{\epsilon_{0} E^{2}}{2}, U_{B}=\frac{\mu_{0} B^{2}}{2}$$
D
$$U_{E}=\frac{E^{2}}{2 \epsilon_{0}}, U_{B}=\frac{B^{2}}{2 \mu_{0}}$$
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