Electromagnetic Waves Physics - Electromagnetic Waves

• A
  The same direction but differ in phase by 90°
• B
  The same direction and are in phase
• C
  Mutually perpendicular directions and differ in phase by 90°
• ✓
  Mutually perpendicular directions and are in phase

Answer: D.

• A
  Troposphere
• B
  Ionosphere
• C
  Stratosphere
• D
  Mesosphere

• A
  Only the radiowaves
• B
  Only the visible light
• C
  Only the γ-rays
• D
  X-rays and ultraviolet rays

• A
  Both magnetic and electric field
• B
  Electric field only
• C
  Magnetic energy
• D
  Electric energy

• A
  5090cm
• B
  4050cm
• C
  4230cm
• D
  3660cm

shows a capacitor made of two circular plates each of radius 12 cm, and separated by 5.0 cm. The capacitor is being charged by an external source (not shown in the figure). The charging current is constant and equal to 0.15A.

1. Calculate the capacitance and the rate of charge of potential difference between the plates.
2. Obtain the displacement current across the plates.
3. Is Kirchhoff’s first rule (junction rule) valid at each plate of the capacitor? Explain.

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• A
  Radius of each circular plate, r = 12 cm = 0.12 m

  Distance between the plates, d = 5 cm = 0.05 m

  Charging current, I = 0.15 A

  Permittivity of free space, $\varepsilon_0=8.85\times10^{-12} \ \text{cm}=0.12 \ \text{m}$

  1. Capacitance between the two plates is given by the relation,

  $\text{C}=\frac{\varepsilon_0\text{A}}{\text{d}}$

  Where,

  A = Area of each plate $=\pi\text{r}^2$

  $\text{C}=\frac{\varepsilon_0\pi\text{r}^2}{\text{d}}$

  $=\frac{8.85\times10^{-12}\times\pi\times12^2}{0.05}$

  $=8.0032\times10^{-12}\text{F}=80.032\text{pF}$

  Charge on each plate, q = CV

  Where,

  V = Potential difference across the plates

  Differentiation on both sides with respect to time (t) gives:

  $\frac{\text{dq}}{\text{dt}}=\text{C}\frac{\text{dV}}{\text{dt}}$

  But, $\frac{\text{dq}}{\text{dt}}=\text{current }(I)$

  $\therefore\frac{\text{dV}}{\text{dt}}=\frac{I}{\text{C}}$

  $\Rightarrow\frac{0.15}{80.032\times10^{-12}}=1.87\times10^9\text{V}/\text{s}$

  Therefore, the change in potential difference between the plates is $1.87\times10^9\text{V}/\text{s}$.

  2. The displacement current across the plates is the same as the conduction current. Hence, the displacement current, i_d is 0.15 A.
  3. Yes

  Kirchhoff’s first rule is valid at each plate of the capacitor provided that we take the sum of conduction and displacement for current.