Electricity and Magnetism II Notes

Course Overview

• Course Title: Electricity and Magnetism II
• Semester: II, B.Ed Regular Group 2022/2023
• Course Tutor: Dr. Lawrence Ochoo
• Main Topics:
  • Gauss’s Law and Applications
  • Capacitors
  • Dielectrics
  • Biot-Savart Law
  • Ampere’s Law
  • Force on current-carrying conductors
  • Electric and Magnetic moments
  • Energy and dipole orientation
  • Sinusoidally varying signals (emf and current)
  • Peak values and RMS values of AC current/emf
  • Effects of alternating currents
  • Impedance and Power in LRC Circuit
  • Rectification of AC

Introduction to Electricity and Magnetism II

• Focuses on simplification of laws used in Electricity and Magnetism I to study electric and magnetic forces.
• Charged particles of matter are emphasized as the foundation of electricity and magnetism.
  • Charges come in two types: positive and negative, exhibiting forces of equal magnitude but opposite direction.

Coulomb’s Law

• The Coulomb’s Law describes the electrostatic force between two point charges: $F = k \frac{q<em>1 q</em>2}{r^2}$
  • Where:
    • $F$ = Force between charges
    • $q1$ and $q2$ = magnitudes of the charges
    • $r$ = distance between the charges
    • $k = \frac{1}{4\pi\epsilon0}$, with $\epsilon0 = 8.85 \times 10^{-12}$ C²/Nm².
• Force Nature:
  • Repulsion: if $q1$ and $q2$ are like charges (positive or negative);
  • Attraction: if $q1$ and $q2$ are unlike charges.

Superposition Principle

• When dealing with multiple charges, the net force on a charge is the vector sum of the individual forces acting on that charge: $F<em>{net} = F</em>1 + F<em>2 + \ldots + F</em>n$
  • Resolve forces into x and y-components for calculation.

Gauss's Law

• Definition: The net electric flux through any closed surface is directly proportional to the net electric charge enclosed:
  $\Phi<em>E = \int E \, dA = \frac{Q</em>{enc}}{\epsilon_0}$
• Flux Density: The electric flux density ($\Phi$) is defined as the number of electric field lines passing through a unit area.
• Applications:
  • Electric field strength calculation around symmetric charge distributions (spherical, cylindrical).

Capacitors and Capacitance

• Function: Devices for storing electric charge.
• Capacitance Definition: The capacity to hold charge per unit voltage: $C = \frac{Q}{V}$
  • Factors Affecting Capacitance:
  • Size of the plates
  • Distance between the plates
  • Presence of dielectric materials.

Alternating Current (AC) and Direct Current (DC)

• Characteristics:
  • AC: Periodically changing direction.
  • DC: Constant direction.
• RMS Values: Used to represent AC current values equivalent to DC for heating effects:
  $I<em>{rms} = \frac{I</em>0}{\sqrt{2}}$
• Rectification: Use of diodes to convert AC to DC, allowing half or full-wave rectification.

Magnetic Forces and Fields

• Definition: Magnetic field strength arises from moving charges or current:
  $F = BIl \, \sin(\theta)$
• Right Hand Rule: Determines direction of the magnetic field generated by a direct current:
  • Thumb: Direction of current; Fingers: Direction of field lines.
• Biot-Savart Law: Calculates the magnetic field generated by current through a small segment of current-carrying wire:
  $dB = \frac{\mu_0}{4 \pi} \frac{I \, dl \times \hat{r}}{r^2}$
• Ampere’s Law: Relates the integrated magnetic field along a closed loop to the current enclosed:
  $\oint B \, dl = \mu<em>0 I</em>{enc}$

Applications of Gauss's Law in Electricity and Magnetic Circuits

• Helps in simplifying calculations for symmetrical charge distributions.
• Crucial for understanding electric fields in conductors and capacitors.