Electricity and Magnetism

Electricity and Magnetism

While civil engineers primarily deal with statics and mechanics, a basic understanding of electricity is essential for building systems, power distribution, and instrumentation.

Electric Charge and Field

Electric Charge ($q$): A fundamental property of matter. Like charges repel, opposite charges attract. Unit: Coulomb (C).

Coulomb's Law: The force between two point charges. $F = k \frac{|q_1 q_2|}{r^2}$ where $k \approx 8.99 \times 10^9 \text{ N}\cdot\text{m}^2/\text{C}^2$.

Electric Field ($\mathbf{E}$): Force per unit charge. $\mathbf{E} = \frac{\mathbf{F}}{q_0}$ For a point charge: $E = k \frac{|q|}{r^2}$.

Electric Potential

Electric Potential ($V$): Electric potential energy per unit charge. $V = \frac{U}{q}$ Unit: Volt (V). 1 V = 1 J/C.

Voltage (Potential Difference): The work done to move a charge between two points. $\Delta V = V_f - V_i = \frac{-\Delta W}{q}$

DC Circuits

Ohm's Law

For many materials (resistors), voltage is proportional to current. $V = IR$ where:

• $V$: Voltage (Volts)
• $I$: Current (Amperes)
• $R$: Resistance (Ohms, $\Omega$)

Resistance

Resistance depends on geometry and resistivity ($\rho$). $R = \rho \frac{L}{A}$

Series and Parallel Circuits

• Series: Same current. $R_{eq} = R_1 + R_2 + \dots$
• Parallel: Same voltage. $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \dots$

Kirchhoff's Rules

1. Junction Rule (Current Law): The sum of currents entering a junction equals the sum leaving. $\sum I_{in} = \sum I_{out}$.
2. Loop Rule (Voltage Law): The sum of potential differences around any closed loop is zero. $\sum \Delta V = 0$.

Magnetic Fields and Forces

Magnetic Field ($\mathbf{B}$): Produced by moving charges (currents) or magnetic materials. Unit: Tesla (T).

Magnetic Force on a Moving Charge: $\mathbf{F} = q \mathbf{v} \times \mathbf{B}$ Magnitude: $F = qvB \sin \theta$.

Magnetic Force on a Current-Carrying Wire: $\mathbf{F} = I \mathbf{L} \times \mathbf{B}$ Magnitude: $F = ILB \sin \theta$.