EM Waves flash cards

1. 1.What is displacement current?

   A current-like term $I_d = \varepsilon_0 \dfrac{d\Phi_E}{dt}$ arising from a changing electric flux; it is not due to flow of charges but produces a magnetic field just like conduction current.

   Hint: Introduced by Maxwell; linked to changing $\Phi_E$.

2. 2.Why did Maxwell introduce displacement current?

   To remove the inconsistency in Ampere's law: for a charging capacitor, no conduction current flows between the plates, yet a magnetic field exists there. The changing electric flux (displacement current) accounts for it.

   Hint: Ampere's law failed at a capacitor gap.

3. 3.Write the expression for displacement current in terms of electric flux.

   $I_d = \varepsilon_0 \dfrac{d\Phi_E}{dt}$, where $\Phi_E$ is the electric flux through the surface.

   Hint: Proportional to rate of change of $\Phi_E$.

4. 4.How do conduction current and displacement current compare in a charging capacitor circuit?

   They are exactly equal in magnitude: $I_c = I_d = \varepsilon_0 \dfrac{d\Phi_E}{dt}$. This keeps the total current continuous across the capacitor gap.

   Hint: Continuity of current is preserved.

5. 5.State the generalised (Ampere–Maxwell) law.

   $\oint \vec{B}\cdot d\vec{l} = \mu_0\left(I_c + \varepsilon_0 \dfrac{d\Phi_E}{dt}\right)$ — magnetic field is produced by conduction current plus displacement current.

   Hint: Ampere's law + displacement current term.

6. 6.What key symmetry did Maxwell's addition of displacement current reveal?

   Just as a changing magnetic field produces an electric field (Faraday), a changing electric field produces a magnetic field. This symmetry between $\vec{E}$ and $\vec{B}$ leads to electromagnetic waves.

   Hint: Changing E ⟶ B, and changing B ⟶ E.

7. 7.List the four Maxwell's equations (qualitatively, by name).

   1) Gauss's law for electricity (electric flux ∝ enclosed charge). 2) Gauss's law for magnetism (net magnetic flux = 0, no monopoles). 3) Faraday's law (changing B ⟶ EMF/E). 4) Ampere–Maxwell law (conduction + displacement current ⟶ B).

   Hint: Two Gauss, one Faraday, one Ampere–Maxwell.

8. 8.What does Gauss's law for magnetism ($\oint \vec{B}\cdot d\vec{A} = 0$) tell us?

   Net magnetic flux through any closed surface is zero, implying isolated magnetic monopoles do not exist; magnetic field lines are always continuous closed loops.

   Hint: No magnetic monopoles.

9. 9.According to Maxwell, what does an accelerating charge produce?

   An accelerating (or oscillating) charge radiates energy in the form of electromagnetic waves. A charge oscillating with frequency $f$ produces EM waves of the same frequency $f$.

   Hint: Only accelerated charges radiate EM waves.

10. 10.Can a charge moving with uniform velocity produce electromagnetic waves?

    No. Only accelerated (or oscillating) charges radiate EM waves. Uniform velocity means zero acceleration, so no radiation.

    Hint: Acceleration is essential.

11. 11.What is an electromagnetic wave?

    A wave consisting of oscillating electric and magnetic fields, mutually perpendicular and perpendicular to the direction of propagation, that travels through space (including vacuum) transporting energy.

    Hint: Coupled oscillating E and B fields.

12. 12.Are electromagnetic waves transverse or longitudinal?

    Transverse — the electric field $\vec{E}$ and magnetic field $\vec{B}$ oscillate perpendicular to the direction of wave propagation.

    Hint: E and B ⟂ propagation direction.

13. 13.State the mutual orientation of $\vec{E}$, $\vec{B}$ and the direction of propagation in an EM wave.

    $\vec{E}$, $\vec{B}$ and the propagation direction are mutually perpendicular. The wave travels along $\vec{E}\times\vec{B}$.

    Hint: $\vec{E}\times\vec{B}$ gives propagation direction.

14. 14.Do electromagnetic waves require a material medium to propagate?

    No. Unlike mechanical waves, EM waves can travel through vacuum. This is how sunlight reaches the Earth through empty space.

    Hint: They travel through vacuum.

15. 15.What is the speed of electromagnetic waves in vacuum, and its formula?

    $c = \dfrac{1}{\sqrt{\mu_0 \varepsilon_0}} \approx 3\times 10^8$ m/s, where $\mu_0$ is the permeability and $\varepsilon_0$ the permittivity of free space.

    Hint: $c=1/\sqrt{\mu_0\varepsilon_0}$.

16. 16.What is the speed of an EM wave in a medium of permittivity $\varepsilon$ and permeability $\mu$?

    $v = \dfrac{1}{\sqrt{\mu \varepsilon}}$. Since $\mu\varepsilon > \mu_0\varepsilon_0$ for a material medium, $v < c$.

    Hint: $v=1/\sqrt{\mu\varepsilon}$, always less than $c$.

17. 17.How is the speed of an EM wave in a medium related to refractive index $n$?

    $v = \dfrac{c}{n}$, where $n = \sqrt{\mu_r \varepsilon_r}$ is the refractive index. For non-magnetic media ($\mu_r \approx 1$), $n \approx \sqrt{\varepsilon_r}$.

    Hint: $v=c/n$ and $n=\sqrt{\mu_r\varepsilon_r}$.

18. 18.State the relation between the magnitudes of $E_0$ and $B_0$ in an EM wave.

    $c = \dfrac{E_0}{B_0}$, i.e. $E_0 = cB_0$. The ratio of the amplitudes of the electric and magnetic fields equals the speed of light.

    Hint: $E_0/B_0 = c$.

19. 19.Which is larger in an EM wave, the electric field amplitude or the magnetic field amplitude (numerically)?

    Numerically the electric field is much larger: $E_0 = cB_0$ with $c \approx 3\times10^8$. But this does not mean E is 'stronger' — the energy is shared equally between the two fields.

    Hint: $E_0 = cB_0$; c is a large factor.

20. 20.Write the standard expressions for the fields of a plane EM wave travelling along the x-axis.

    $E_y = E_0 \sin(kx - \omega t)$ and $B_z = B_0 \sin(kx - \omega t)$, where the E field is along y and B field along z.

    Hint: E and B in phase, perpendicular directions.

21. 21.Are $\vec{E}$ and $\vec{B}$ in phase in an electromagnetic wave?

    Yes. In a plane EM wave in vacuum, $\vec{E}$ and $\vec{B}$ oscillate in phase — they reach their maxima and zeros at the same instants.

    Hint: They peak together.

22. 22.How are the frequency and wavelength of an EM wave related to its speed?

    $c = f\lambda$ (in vacuum), where $f$ is frequency and $\lambda$ is wavelength. In a medium $v = f\lambda$, with frequency unchanged and wavelength reduced.

    Hint: $c=f\lambda$; f stays fixed across media.

23. 23.When an EM wave enters a denser medium, which quantities change?

    Speed and wavelength decrease (both by factor $n$); frequency remains unchanged because it is set by the source.

    Hint: Frequency constant; v and λ drop.

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