Electric Fields Lecture Notes

Introduction to Electric Fields

• Electric Field (E): Represents how an electric force (F) acts on a test charge (Q).
• Formula: ( E = \frac{F}{Q} )
  • Measured in Newtons per Coulomb (N/C)
• Vector Nature: Similar to force, has direction and magnitude.

Behavior with Charges

• Positive Test Charge: Moves in the direction of the electric field.
• Negative Test Charge: Moves opposite to the direction of the electric field.

Electric Field Creation

• Positive Charge: Electric field radiates outward.
• Negative Charge: Electric field radiates inward.

Calculating Electric Field from Point Charge

• Equation: ( E = \frac{kQ}{r^2} )
  • ( k = 9 \times 10^9 ) N·m²/C²
  • ( r ): Distance from charge.
  • ( Q ): Charge magnitude.

Direction of Electric Fields Example

• Positive Charge (Q): Field points away from the charge.
  • Direction varies (north, west, southeast, etc.)
• Negative Charge (Q): Field points towards the charge.
  • Similar directional considerations.

Word Problem Walkthroughs

Example 1

• Problem: Force of 100 N north on a -20 μC point charge.
• Solution Process: (Electric Field E)
  • Direction: Opposite to force, hence south.
  • Magnitude: ( E = \frac{F}{|Q|} = \frac{100}{20 \times 10^{-6}} = 5 \times 10^6 ) N/C.

Example 2

• Problem: Balance between electric force and gravity.
• Setup: Positive charge in an electric field.
• Solution Process: (Mass of Charge)
  • Equate electric force to weight: ( E \cdot Q = mg ). Calculate mass.

Example 3

• Problem: Electron acceleration in an electric field.
• Solution Process: (Magnitude and Direction of E)
  • Direction: Opposite to electron's force (west).
  • Magnitude: Uses formula ( E = \frac{ma}{Q} ).

Practical Calculations

• Electric Field Units Conversion: (μC to C, etc.)
• Example Calculations: Electric field at various points around charges.

Advanced Scenarios

Example 6

• Problem: Multiple charges interaction.
• Analysis: Use electric field formula and vector addition.

Example 8

• Problem: Zero electric field point between charges.
• Solution Insight: Identify balance point based on charge magnitudes and distances.

Review Concepts

• Key Relationships: (E, F, Q, k)
• Important Constants:
  • Electron and proton mass and charge values.
  • Micro, nano, milli conversions for charge units.

Summary

• Understanding the direction and magnitude of electric fields is crucial for solving electrostatics problems.
• Problem-solving often involves balancing forces and understanding the behavior of charges in fields.