Electric Fields

Introduction

• Focus on non-uniform electric fields.
• Previous knowledge on uniform fields (parallel plates).
• In uniform parallel plates, electric field (E) and force (F) are constant.
• Non-uniform fields involve varying forces and accelerations.

Interaction of Point Charges

• Example of two point charges examining force interaction.
• Charges must both be non-zero to exert force on each other.
• Equal and opposite forces due to interaction (Newton's third law).
• Higher charge results in a greater force.
• Attraction and repulsion indicated by direction of force arrows.
• Closer distance between charges increases the force.

Coulomb’s Law

• Fundamental equation for force between two point charges: [ F = \frac{k q_1 q_2}{r^2} ]
• Proportionality:
  • Directly proportional to product of charges (( q_1 ) and ( q_2 )).
  • Inversely proportional to the square of the separation distance (( r )).
• Constant ( k = \frac{1}{4 \pi \epsilon_0} ), with ( \epsilon_0 ) being the permittivity of free space.

Conceptual Understanding

• Force (F) measured between point charges in newtons (N).
• Coulomb’s Law: Electric force proportional to product of charges and inversely proportional to the square of distance.
• Importance of the point charge for Coulomb’s Law.
• Evaluation of forces through vector diagrams rather than negative signs in the equation.

Electric Field (E)

• Derived from force per unit positive test charge: [ E = \frac{F}{q} ]
• Electric field around a charge visualized via electric field lines.
• Electric field strength depends on charge magnitude and distance.

Electric Field Strength Equation

• Electric field strength (due to charge ( q_1 )) is: [ E_1 = \frac{k q_1}{r^2} ]
• Independence from the test charge (( q_2 )) simplifies understanding.

Units of Electric Field

• Two main units:
  • Newton per Coulomb (N/C)
  • Volt per Meter (V/m)
• Equation ([ E = F/q ]) leads to ([ N/C ])
• Relation to potential difference over distance ( [ V/D ]) leads to ([ V/m ]).

Non-uniform vs. Uniform Fields

• Explanation of non-uniform fields with varying force intensity.
• Uniform fields (parallel plates) have constant electric field strength.

Graphical Representation

• Graphs of electric field strength vs. distance (inverse square law).
• Reminder not to use ( V/D ) unless dealing with uniform parallel plates.

Reminder: Non-uniform fields vary in strength based on distance from charge.