For the plane electromagnetic wave given by $\mathrm{E}=\mathrm{E}_{0} \sin (\omega \mathrm{t}-\mathrm{kx})$ and $\mathrm{B}=\mathrm{B}_{0} \sin (\omega \mathrm{t}-\mathrm{kx})$, the ratio of average electric energy density to average magnetic energy density is

JEE Main · 2023 · 06 Apr 2023 · Shift 1 · EM Waves

For the plane electromagnetic wave given by

E = E_{0} sin (ω t - kx)

and

B = B_{0} sin (ω t - kx)

, the ratio of average electric energy density to average magnetic energy density is

(A)1✓ Correct
(B) $1/2$
(C)2
(D)4

Answer: (A)

Solution

The average electric energy density is

\frac{1}{2} ϵ_{0} E_{rms}^{2}

and the average magnetic energy density is

\frac{B _{rms}^{2}}{2 μ _{0}}

. Their ratio is:

\frac{Electric energy density}{Magnetic energy density} = \frac{\frac{1}{2} ϵ _{0} E _{rms}^{2}}{\frac{B _{rms}^{2}}{2 μ _{0}}} = (\frac{E _{rms}}{B _{rms}})^{2} μ_{0} ϵ_{0}

For electromagnetic waves,

E / B = c = 1/ μ_{0} ϵ_{0}

, so

(E / B)^{2} = c^{2} = 1/ (μ_{0} ϵ_{0})

. Therefore:

\frac{Electric energy density}{Magnetic energy density} = \frac{c ^{2}}{c ^{2}} = 1

JEE Main · 2023 · 06 Apr 2023 · Shift 1 · Single correct option

Practise more: all JEE Main PYQs on EM Waves →

More JEE Main questions on EM Waves

The electric field of a plane electromagnetic wave, travelling in an unknown non-magnetic medium is given by,
$E_{y} = 20 sin (3 \times 1 0^{6} x - 4.5 \times 1 0^{14} t) V / m$
(where $x, t$ and ot …
JEE Main 2026View solution →
A laser beam has intensity of $4.0 \times 1 0^{14} W / m^{2}$ . The amplitude of magnetic field associated with beam is ______ T. (Take $ϵ_{0} = 8.85 \times 1 0^{- 12} C^{2} / Nm^{2}$ and $c = 3 \times 1 0^{8} m / s$ )
JEE Main 2026View solution →
An electromagnetic wave of frequency 100 MHz propagates through a medium of conductivity, $σ = 10 mho / m$ . The ratio of maximum conducting current density to maximum displacement current density is ____ .

$[$ Take …
JEE Main 2026View solution →
The equation of the electric field of an electromagnetic wave propagating through free space is given by :
$E = 377 sin (6.27 \times 1 0^{3} t - 2.09 \times 1 0^{- 5} x)$ N/C
The average power of the electromagnetic wave is $(\frac{1}{α})$ W/m $^{2}$ . T …
JEE Main 2026View solution →
The ratio of speeds of electromagnetic waves in vacuum and a medium, having dielectric constant $k = 3$ and permeability of $μ = 2 μ_{0}$ , is ( $μ_{0} =$ permeability of vacuum)
JEE Main 2026View solution →
The electric field of an electromagnetic wave travelling through a medium is given by
$E (x, t) = 25 sin (2.0 \times 1 0^{15} t - 1 0^{7} x) \overset{n}{^}$
then the refractive index of the medium is ______.
(All given measurement are in SI units)
JEE Main 2026View solution →