Electromagnetism: Charges and Forces

• Electromagnetism is a fundamental force of nature, involving electric and magnetic phenomena
• The force acts between electrically charged particles
• Interactions between charged particles are mediated through electromagnetic fields
• Electric and magnetic fields manifest these interactions

Charges and Forces

• Electric charge is a fundamental property of matter, existing as positive or negative
• Like charges repel each other, while opposite charges attract
• Coulomb's Law describes the force between two charges
• Coulomb's Law: Force is proportional to the product of charges and inversely proportional to the square of the distance
• The force acts along the line connecting the two charges
• Coulomb's Law formula: F = k * |q1*q2| / r^2, where F is force, q1 and q2 are charge magnitudes, r is distance, and k is Coulomb's constant

Electric Field

• An electric field is a vector field surrounding an electric charge, which exerts force on other charges
• Electric field E at a point is force F per unit positive charge q, E = F/q
• The electric field due to a point charge q at distance r is E = k * q / r^2
• Electric field lines represent the field's direction and strength

Electric Potential

• Electric potential (voltage) is electric potential energy per unit charge
• Potential difference is work per unit charge to move a charge between two points
• Voltage is measured in volts (V), where 1 volt = 1 joule/coulomb
• Electric potential V due to point charge q at distance r is V = k * q / r

Capacitance

• A capacitor stores electrical energy in an electric field, typically using conductive plates separated by a dielectric
• Capacitance (C) is the ratio of charge (Q) to voltage (V): C = Q/V
• Capacitance is measured in farads (F)
• Energy stored in a capacitor: U = 1/2 * C * V^2

Current and Resistance

• Electric current is the rate of electric charge flow, measured in amperes (A)
• 1 ampere = 1 coulomb/second
• Current is conventionally the flow of positive charge
• Resistance (R) is the opposition to current flow, measured in ohms (Ω)
• Ohm's Law: Voltage (V) across a resistor is proportional to current (I): V = I * R
• Resistivity (ρ) is a material property determining resistance
• Resistance of a wire: R = ρ * L / A, where L is length and A is cross-sectional area

Electric Circuits

• Electric circuits are closed loops allowing current flow, containing voltage sources, resistors, and capacitors
• Kirchhoff's Laws analyze circuits:
  • Kirchhoff's Current Law (KCL): Sum of currents entering a node equals the sum leaving
  • Kirchhoff's Voltage Law (KVL): Sum of voltage drops around a closed loop is zero
• Resistors in series add directly: R_total = R1 + R2 + ...
• Resistors in parallel combine as: 1/R_total = 1/R1 + 1/R2 + ...

Magnetism

• Magnetism is a force caused by moving electric charges
• Moving charges create magnetic fields
• Magnetic fields exert forces on other moving charges

Magnetic Field

• A magnetic field (B) is a vector field that exerts force on moving charges
• The direction of the magnetic field is defined as the direction a compass needle points
• Magnetic field lines visualize the magnetic field
• Lorentz force: F = q * (v x B), where F is the magnetic force on a moving charge q with velocity v in a magnetic field B
• The magnetic force is perpendicular to both velocity and magnetic field

Sources of Magnetic Field

• A current-carrying wire creates a magnetic field
• Magnetic field due to a long straight wire: B = (μ0 * I) / (2πr), where I is current, r is distance, μ0 is permeability of free space
• Current loops create magnetic dipole fields, similar to bar magnets
• Solenoids (coils) produce strong, uniform magnetic fields inside

Magnetic Materials

• Materials are classified by magnetic properties:
• Ferromagnetic materials (e.g., iron) can be strongly magnetized
• Paramagnetic materials are weakly attracted to magnetic fields
• Diamagnetic materials are weakly repelled by magnetic fields

Electromagnetic Induction

• A changing magnetic field induces an electric field through electromagnetic induction
• Faraday's Law: Induced EMF in a closed circuit equals the negative rate of change of magnetic flux
• EMF = -dΦ/dt, where Φ is magnetic flux
• Lenz's Law: Induced current opposes the change in magnetic flux

Inductance

• Inductance (L) measures a circuit's opposition to current changes, measured in henries (H)
• An inductor stores energy in a magnetic field
• Voltage across an inductor: V = L * (dI/dt)
• Energy stored in an inductor: U = 1/2 * L * I^2

AC Circuits

• Alternating current (AC) periodically reverses direction
• AC voltage and current vary sinusoidally
• AC circuits are characterized by impedance (Z), the AC equivalent of resistance
• Impedance includes resistance (R), inductive reactance (XL), and capacitive reactance (XC)
• XL = ωL (ω is angular frequency, L is inductance)
• XC = 1/(ωC) (C is capacitance)
• Total impedance in series RLC circuit: Z = sqrt(R^2 + (XL - XC)^2)

Electromagnetic Waves

• Accelerating charges produce electromagnetic waves that are transverse, with oscillating electric and magnetic fields
• Fields are perpendicular to each other and to wave's direction
• Electromagnetic waves travel at the speed of light (c) in a vacuum, c ≈ 3.0 x 10^8 m/s
• The electromagnetic spectrum includes radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays
• Energy of an electromagnetic wave: E = h*f (h is Planck's constant)
• Wavelength (λ) and frequency (f) are related by c = λ * f