Lecture5ElectricField

Introduction to Electromagnetism

  • Focus areas: electrostatics (electric fields from stationary charges) and magnetostatics (magnetic fields from steady currents).

  • Key concepts: charges and currents.

Charges and Currents

Overview

  • Charges (q) and currents (I) are fundamental in electromagnetic theory.

Charges (2.1)

  • Electric charge (units: Coulombs [C]) determines motion in electromagnetic fields.

    • Types of charges: positive (e.g., protons), negative (e.g., electrons).

    • Like charges repel; opposite charges attract.

  • Charge behaves like mass in Newtonian gravity, affecting motion in defined fields.

  • Neutral objects have no net charge (zero net charge).

  • Charge is conserved in closed systems.

  • Charges result in electric fields, essential for electrostatics.

Electric Field (3)

Definition and Law

  • Electric field (E) arises from stationary charge; formula resembles Newton's gravitational field law:

    • From a charge q at origin:[ E(x,y,z) = \frac{1}{4 \pi \epsilon_0} \frac{q}{|\mathbf{r}|^2} \hat{r} ]

  • Constants:

    • Gravitational constant (G) vs. permittivity of free space ((\epsilon_0)).

      • k = (\frac{1}{4 \pi \epsilon_0} = 8.988 \times 10^9 \text{ Nm}^2/ ext{C}^2).

  • Electric field equation:[ E = k \frac{q}{|\mathbf{r}|^2} \hat{r} ]

Variation in Position

  • Electric field can be evaluated from any position, not limited to the origin.

  • Distance vector (\mathbf{R}) calculated from source to point P: [ E = kQ \frac{\mathbf{R}}{R^2} \hat{R} ]

Force on Charged Particles

  • The force (F) on a charge Q at point P relates to the electric field: [ F = QE ]

    • Similar to Newton's gravity law: [ F = mg ]

  • Coulomb’s law expression for interaction between charges: [ F = kQq \frac{\mathbf{R}}{R^2} ]

Coulomb's Law

  • Force on charge due to stationary charges: [ F = \sum_{i=1}^n k \frac{Qq_i}{R^2_i} \hat{R_i} ]

    • Match parallels with Newtonian gravity laws.

  • Simple Coulomb’s law: [ F = kqQ \frac{1}{R^2} ]

Overview of Electric Field Contributions

  • An electric field is defined at any point, considering all relevant source charges.

  • Key concept: electric fields created by both stationary charges and moving charged particles.

  • Motion of a charged particle in a field can be analyzed using Newton's second law through the force derived from Coulomb's law.