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Electrostatic Potential and Capacitance

Electrostatic potential and capacitance are fundamental concepts in electromagnetism. Here’s a brief overview:

Electrostatic Potential

  • Definition: Electrostatic potential at a point is the work done to bring a unit positive charge from infinity to that point, without any acceleration. It’s a scalar quantity and is measured in volts (V).
  • Formula: For a point charge QQQ, the electrostatic potential VVV at a distance rrr from the charge is given by: V=kQrV = \frac{kQ}{r}V=rkQ​ where kkk is Coulomb’s constant (k≈8.99×109 N m2/C2k \approx 8.99 \times 10^9 \, \text{N m}^2/\text{C}^2k≈8.99×109N m2/C2).

Capacitance

  • Definition: Capacitance is the ability of a system to store charge per unit voltage. It is measured in farads (F).
  • Formula: The capacitance CCC of a capacitor is defined by:C=QVC = \frac{Q}{V}C=VQ​where QQQ is the charge stored and VVV is the voltage across the capacitor.
  • For a Parallel Plate Capacitor: The capacitance is given by:C=ε0AdC = \frac{\varepsilon_0 A}{d}C=dε0​A​where ε0\varepsilon_0ε0​ is the permittivity of free space (ε0≈8.85×10−12 F/m\varepsilon_0 \approx 8.85 \times 10^{-12} \, \text{F/m}ε0​≈8.85×10−12F/m), AAA is the area of one of the plates, and ddd is the separation between the plates.

If you have specific questions or need to go deeper into any part of these topics, let me know!

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