Electricity and Magnetism II Notes

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

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.

The Coulomb’s Law describes the electrostatic force between two point charges: F = k \frac{q1 q2}{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.

When dealing with multiple charges, the net force on a charge is the vector sum of the individual forces acting on that charge: F{net} = F1 + F2 + \ldots + Fn
- Resolve forces into x and y-components for calculation.

Definition: The net electric flux through any closed surface is directly proportional to the net electric charge enclosed:
\PhiE = \int E \, dA = \frac{Q{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).

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.

Characteristics:
- AC: Periodically changing direction.
- DC: Constant direction.
RMS Values: Used to represent AC current values equivalent to DC for heating effects:
I{rms} = \frac{I0}{\sqrt{2}}
Rectification: Use of diodes to convert AC to DC, allowing half or full-wave rectification.

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 = \mu0 I{enc}