Electric Potential Energy Lecture Notes

Introduction to Electric Potential Energy

• Electric potential energy is the topic of discussion.
• Example setup: Two parallel plates, one positive and one negative.
• Electric field extends from positive to negative plate.
• Positive charge between plates experiences a force in the direction of the electric field (negative y-direction).
• Negative charge experiences a force opposite to the electric field.

Calculating Electric Potential Energy

• Work and Potential Energy:

  • Work from point A to B = negative change in potential energy.
  • Potential energy (PE) or U: differentiate from gravitational potential energy (GPE) which uses mgh.
  • Use U for electric potential energy in this context.

• Formula Derivation:

  • Work = force x displacement.
  • Electric force = electric field (E) x charge (q).
  • Displacement from A to B = yB - yA.
  • Final formula: Electric potential energy = -Eqy (similar to GPE = mgh).

Example Problem

• 50 micro coulomb charge moves from point A (80 cm) to B (20 cm) above the plate.
• Electric field = 2 x 10^6 N/C.
• Calculate Electric Potential Energy at A and B:
  • Use formula: U = -Eqy.
  • At A: U = 80 Joules.
  • At B: U = 20 Joules.

Change in Potential and Kinetic Energy

• Electric potential energy decreases from A to B (U changes from 80 to 20 Joules).
• Kinetic energy increases as electric force accelerates the charge.
• Work done is positive as displacement and force are in the same direction.

Calculating Work Done

• Work = negative change in potential energy.
• Example calculation results in 60 Joules of work.

Electric Potential

• Electric potential (V) = electric potential energy (U) / charge (q).
• Units: Joules (U) and Volts (V).
• At A: V = 1.6 megavolts (1.6 x 10^6 V).
• At B: V = 400 kilovolts (400,000 V).

Gravitational vs. Electric Potential Energy

• Both forms depend on height (y) or position.
• Gravitational: GPE = mgh.
• Electric: U = Eqy.

Additional Example Problems

• Problem 2: Calculating electric potential energy given electric potential and charge (e.g., U = qV).

• Problem 3: Calculating electric field and electric potential between charged plates.

• Electric Field Calculation:

  • E = voltage / distance.
  • Example: E = 10,000 V/m or 10 V/mm.

• Electric Potential Energy Calculation at a Point:

  • U = qV.
  • Verify using U = -Eqy for consistency.

Summary

• Electric potential energy is analogous to gravitational potential energy, both dependent on positional factors.
• Understanding direction and sign conventions is crucial (negative for direction).
• Multiple approaches to calculating electric potential energy and work.
• Familiarity with units and conversions (micro coulombs, volts, joules) is necessary.