Lecture on Electric Potential V

Introduction

• Electric Potential V is considered one of the most confusing concepts in physics.
• It is related to Electric Potential energy but is distinct from it.
• Electric Potential V is an abstract number associated with points in space.

Nature of Electric Potential (V)

• In an empty universe, the V value at every point would be zero.
• When a charge is introduced, the V value becomes non-zero around it.
• Closer to the charge, V values increase, and they decrease with distance.

Importance of Electric Potential

• Units: Joules per Coulomb.
• Joules are a measure of energy, indicating that Electric Potential is related to energy.
• If V at a point is 100 Joules per Coulomb, placing a 2 Coulomb charge there results in 200 Joules of energy.

Connection to Electric Potential Energy

• Electric Potential Energy (PE), sometimes denoted as U, is calculated using V.
• Formula: PE = Q × V
  • Q is the charge placed at the point in space.
  • V is the Electric Potential at that point.

Calculating Electric Potential (V)

• Formula: V = (K × Q) / r
  • K is the Electric constant (9 × 10⁹ N m²/C²).
  • Q is the charge creating the V value.
  • r is the distance from the charge to the point in space (not necessarily a radius).
• Example Calculation:
  • If Q is 1 nanoCoulomb (10⁻⁹ C) and r is 9 cm (.09 m), V equals 100 Joules per Coulomb.

Units and Conversion

• V results in Joules per Coulomb.
  • Newton × meter = Joules confirms the units.
• V varies inversely with distance r.
  • Doubling r halves V, halving r doubles V.

Electric Potential vs. Voltage

• V and Voltage are sometimes used interchangeably but differ technically.
• Voltage is the change in Electric Potential between two points.
• Both have units of Joules per Coulomb, termed as Volts when referred to as a change.

Practical Considerations

• Knowing V helps in understanding Potential energy when placing charges.
• Be wary of confusing Electric Potential with Voltage in calculations.

Summary

• Electric Potential V provides a way to determine how much Potential energy could be stored by placing a charge at a point.
• It allows for a quick calculation of Electric Potential energy in a given configuration.