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EM Waves formulas

Master EM Waves through 22 JEE Advanced-level formulas, systematically structured with every variable spelled out. Revise concept-wise, identify the areas where you need improvement, and focus your preparation with greater precision.

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EM Waves, every formula

22 formulas, typeset and free. Print it, or keep it open beside your practice.

Speed of light (vacuum)
$c = \frac{1}{μ _{0} ε _{0}} = 3 \times 1 0^{8} m/s$
Q1MCQSpeed of light
The speed of light in vacuum is:
- A
  $\dfrac{1}{\sqrt{\mu_0\varepsilon_0}}$
- B
  $\sqrt{\mu_0\varepsilon_0}$
- C
  $\mu_0\varepsilon_0$
- D
  $\dfrac{1}{\mu_0\varepsilon_0}$
Speed in a medium
$v = \frac{1}{μ ε} = \frac{c}{n}$
Q1MCQSpeed in medium
The speed of an EM wave in a medium of refractive index $n$ is:
- A
  $\dfrac{c}{n}$
- B
  $cn$
- C
  $c$
- D
  $\dfrac{n}{c}$
Field amplitude relation
$E_{0} = c B_{0}$
Q1MCQAmplitude relation
For an EM wave, the field amplitudes satisfy:
- A
  $E_0=cB_0$
- B
  $B_0=cE_0$
- C
  $E_0=B_0$
- D
  $E_0 B_0=c$
Instantaneous field ratio
$\frac{E}{B} = c$
Q1MCQField ratio
At any instant, the ratio $E/B$ in an EM wave equals:
- A
  $c$
- B
  $\dfrac{1}{c}$
- C
  $c^{2}$
- D
  $1$
Wave relation
$c = ν λ$
Q1MCQWave relation
The wave relation for light is:
- A
  $c=\nu\lambda$
- B
  $c=\dfrac{\nu}{\lambda}$
- C
  $c=\dfrac{\lambda}{\nu}$
- D
  $\nu=c\lambda$
Displacement current
$i_{d} = ε_{0} \frac{d ϕ _{E}}{d t}$
Q1MCQDisplacement current
The displacement current is:
- A
  $\varepsilon_0\dfrac{d\phi_E}{dt}$
- B
  $\mu_0\dfrac{d\phi_E}{dt}$
- C
  $\dfrac{d\phi_B}{dt}$
- D
  $\varepsilon_0\phi_E$
Poynting vector
$S = \frac{1}{μ _{0}} (E \times B)$
Q1MCQPoynting vector
The Poynting vector is:
- A
  $\dfrac{1}{\mu_0}(\vec E\times\vec B)$
- B
  $\vec E\cdot\vec B$
- C
  $\mu_0(\vec E\times\vec B)$
- D
  $\dfrac{\vec E}{\vec B}$
Average electric energy density
$u_{E} = \frac{1}{4} ε_{0} E_{0}^{2}$
Q1MCQTotal energy density
The total average energy density of an EM wave is:
- A
  $\tfrac12\varepsilon_0 E_0^{2}$
- B
  $\tfrac14\varepsilon_0 E_0^{2}$
- C
  $\varepsilon_0 E_0^{2}$
- D
  $\dfrac{B_0^{2}}{4\mu_0}$
Average magnetic energy density
$u_{B} = \frac{B _{0}^{2}}{4 μ _{0}}$
Q1MCQEnergy split
In an EM wave, the electric and magnetic energy densities are:
- A
  equal
- B
  in ratio $2:1$
- C
  in ratio $1:2$
- D
  unrelated
Total average energy density
$u = \frac{1}{2} ε_{0} E_{0}^{2} = \frac{B _{0}^{2}}{2 μ _{0}}$
Q1MCQIntensity
The intensity of an EM wave is:
- A
  $\tfrac12\varepsilon_0 E_0^{2}c$
- B
  $\varepsilon_0 E_0^{2}$
- C
  $\dfrac{E_0^{2}}{c}$
- D
  $\tfrac12\varepsilon_0 E_0^{2}$
Intensity of an EM wave
$I = \frac{1}{2} ε_{0} E_{0}^{2} c$
Q1MCQRadiation pressure (absorb)
The radiation pressure on a perfectly absorbing surface is:
- A
  $\dfrac{I}{c}$
- B
  $\dfrac{2I}{c}$
- C
  $Ic$
- D
  $\dfrac{c}{I}$
Radiation pressure (absorbing)
$P = \frac{I}{c}$
Q1MCQRadiation pressure (reflect)
The radiation pressure on a perfectly reflecting surface is:
- A
  $\dfrac{2I}{c}$
- B
  $\dfrac{I}{c}$
- C
  $Ic$
- D
  $0$
Radiation pressure (reflecting)
$P = \frac{2 I}{c}$
Q1MCQRadiation momentum
The momentum carried by radiation of energy $U$ is:
- A
  $\dfrac{U}{c}$
- B
  $Uc$
- C
  $\dfrac{c}{U}$
- D
  $U$
Momentum of radiation
$p = \frac{U}{c}$
Q1MCQDirections
In an EM wave, $\vec E$, $\vec B$, and the propagation direction are:
- A
  mutually perpendicular
- B
  parallel
- C
  antiparallel
- D
  at $45^{\circ}$
Directions in an EM wave
$E ⊥ B ⊥ c$
Q1MCQAmpere–Maxwell
The Ampere–Maxwell law adds which term to Ampere's law?
- A
  $\mu_0\varepsilon_0\dfrac{d\phi_E}{dt}$
- B
  $\dfrac{d\phi_B}{dt}$
- C
  $\mu_0 I$
- D
  $0$
Ampere–Maxwell law
$\oint B \cdot d l = μ_{0} (I + ε_{0} \frac{d ϕ _{E}}{d t})$
Q1MCQRefractive index
The refractive index in terms of relative permeability/permittivity is:
- A
  $\sqrt{\mu_r\varepsilon_r}$
- B
  $\mu_r\varepsilon_r$
- C
  $\dfrac{1}{\sqrt{\mu_r\varepsilon_r}}$
- D
  $\mu_r+\varepsilon_r$
Refractive index
$n = \frac{c}{v} = μ_{r} ε_{r}$
Q1MCQSpectrum order
Which has the highest frequency?
- A
  gamma rays
- B
  radio waves
- C
  visible light
- D
  microwaves
Spectrum order (increasing frequency)
$radio < micro < IR < visible < UV < X < γ$
Q1MCQVisible range
The wavelength range of visible light is approximately:
- A
  $400$–$700$ nm
- B
  $1$–$10$ nm
- C
  $1$–$10\ \mu$m
- D
  $10$–$100$ nm
Visible range
$400 nm < λ < 700 nm$
Q1MCQPhoton energy
The energy of an EM-wave photon is:
- A
  $\dfrac{hc}{\lambda}$
- B
  $\dfrac{h\lambda}{c}$
- C
  $hc\lambda$
- D
  $\dfrac{\lambda}{hc}$
Photon energy
$E = h ν = \frac{h c}{λ}$
Q1MCQPoynting = intensity
The time-averaged Poynting vector gives the:
- A
  intensity
- B
  frequency
- C
  wavelength
- D
  charge
Energy carried per unit area per time
$⟨ S ⟩ = I$
Q1MCQTransverse
EM waves are:
- A
  transverse (can be polarised)
- B
  longitudinal
- C
  non-propagating
- D
  unpolarisable
Transverse nature
$EM waves are transverse (can be polarised)$

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EM Waves formulas

EM Waves, every formula

Speed of light (vacuum)

Speed in a medium

Field amplitude relation

Instantaneous field ratio

Wave relation

Displacement current

Poynting vector

Average electric energy density

Average magnetic energy density

Total average energy density

Intensity of an EM wave

Radiation pressure (absorbing)

Radiation pressure (reflecting)

Momentum of radiation

Directions in an EM wave

Ampere–Maxwell law

Refractive index

Spectrum order (increasing frequency)

Visible range

Photon energy

Energy carried per unit area per time

Transverse nature

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