Lecture on Electric Potential and Electric Potential Energy

Definitions

• Electric Potential (V): Potential energy per unit charge.
  • Formula: $V = \frac{U}{q}$, where $U$ is potential energy and $q$ is charge.
• Electric Potential Energy (U): The energy stored due to the position in an electric field.
• Types of Potential Energy:
  • Elastic Potential Energy: Energy stored in elastic materials like springs.
  • Gravitational Potential Energy: Energy due to an object's position above ground.
  • Electric Potential Energy: Energy due to charge positions in an electric field.

Measurements and Units

• Electric Potential (V): Measured in volts (V).
  • 1 Volt = 1 Joule/Coulomb.
  • Example: 5V = 5J/C for a 1 Coulomb charge.

Voltage (Potential Difference)

• Voltage (ΔV): The difference in electric potential between two points.
  • Formula: $ V_{BA} = V_B - V_A $
  • Example: V is 80V at point B and 20V at point A, ΔV = 60V

Example Problems and Analysis

1. Voltage Calculation

• Points A (20V) and B (80V)
  • $V_{BA} = 80V - 20V = 60V$
  • $V_{AB} = 20V - 80V = -60V$
• Points A (-30V) and B (90V)
  • $V_{BA} = 90V - (-30V) = 120V$
  • $V_{AB} = -30V - 90V = -120V$
• Direction and Significance:
  • Positive ΔV indicates increasing electric potential.

2. Work Done by Electric Field

• Work formula relating to electric potential: $ W = -qΔV $
• Example:
  • Move -500 μC charge across 300V potential difference.
  • Work: $ W = -qΔV = -(-500 \times 10^{-6} C) * 300V = 0.15J $

3. Electric Field Effects on Charge

• **Positive Charge Mechanics: **
  • Moves from high potential to low potential
  • Accelerated by electric field
  • Potential Energy (PE) decreases as Kinetic Energy (KE) increases.
  • Work done by electric field is positive.
• Negative Charge Mechanics:
  • Moves from low potential to high potential.
  • Slowed down by electric field.
  • PE increases as KE decreases.
  • Work done by electric field is negative.
• Example Calculation:
  • Move -50 μC charge from -50V to 250V.
  • Work: $ W = -QΔV = -(-50 \times 10^{-6} C * 300V) = 0.015J $
  • Kinetic Energy relation: $ KE = \frac{1}{2}mv^2 $
  • Final Speed: $ v = 54.77 \frac{m}{s} $

Key Formulas and Concepts

• Work-Energy Principle: $ W = ΔKE = -ΔPE $
• Voltage-Potential Energy Relation: $ ΔV = \frac{ΔU}{q} $
• Direction of Electric Field and Charge Movement:
  • Positive charges move high V to low V
  • Negative charges move low V to high V

Summary

• Electric potential and electric potential energy are crucial concepts in understanding electric fields and forces.
• Voltage is an important measure of potential difference and is fundamental in circuit analysis.
• The relationship between potential energy, voltage, and work done by electric fields helps in solving practical physics problems.