Electrostatics and Magnetism

• Electrostatics: Study of stationary charges.
• Basic properties:
  • Proton (+), electron (-), opposites attract.
  • Stable matter occurs when charges balanced; imbalance → unstable.
• Charge generation:
  • Friction can transfer electrons (e.g., shuffle feet on carpet → body gains negative charge).
  • Grounding: returning charge to Earth.
• Static electricity:
  • More significant in dry air; humidity aids separation and maintenance of charge.
• Unit: Coulomb (C)
  • Electron charge: $e = 1.6 \times 10^{-19} C$
• Conservation: Charge cannot be created or destroyed.
• Mass effect: Electrons accelerate more than protons due to smaller mass.

Insulators and Conductors

• Insulators:
  • Do not distribute charge; electrons bound to nuclei.
  • Most nonmetals.
  • Used in dielectrics for capacitors to prevent grounding.
• Conductors:
  • Distribute charge across surface.
  • Free electrons allow transfer.
  • Metals, ionic solutions; used in circuits and electrochemical cells.

• Coulomb's law: $F_e = k \frac{q_1 q_2}{r^2}$
  • $k = 9 \times 10^9\ \mathrm{Nm^2/C^2} = \frac{1}{4 \pi \varepsilon_0}$
  • $\varepsilon_0 = 8.85 \times 10^{-12}\ C^2/N\cdot m^2$
  • Like charges repel, opposite attract.
  • Example: + and - separated distance d → 2d → force = 1/4 original.

Electric Field

• Created by charge Q, exerts force on other charges.
• Magnitude: $E = \frac{F_e}{q} = k\frac{Q}{r^2}$
• Vector points in direction a positive test charge would move:
  • Positive source → repulsive, outward
  • Negative source → attractive, inward
• Field lines:
  • Imaginary lines showing charge motion.
  • Closer lines → stronger field.
  • test charge → force same direction; - test charge → opposite.

    

• $U = k \frac{Qq}{r}$
  • Positive for like charges, negative for opposites.
• Relation to work: $\Delta U = W = F d \cos \theta = F r = k \frac{Qq}{r}$
• Attractive forces → closer = more stable.
• Increasingly negative values = decreasing potential energy.

• Electric potential: $V = \frac{U}{q}$
  • Units: volts (V) = J/C
  • Scalar; sign follows Q.
  • $V = k \frac{Q}{r}$
• Voltage / Potential difference: $\Delta V = V_b - V_a = \frac{W_{ab}}{q}$
• Charge movement:
  • Negative → lower to higher potential
  • Positive → higher to lower potential
• Mnemonic: Battery + = high potential, - = low; + moves +→-, - moves -→+

• Equipotential lines:
  • Line where potential same → ΔV = 0
  • No work along line
  • Concentric circles (3D: spheres)
• Electric dipoles:
  • Two equal opposite charges separated by distance d.
  • V = $k \frac{qd}{r^2} \cos \theta$
  • Dipole moment: $p = q d$ (vector along charge axis)
  • Perpendicular bisector → potential = 0
  • Electric field magnitude on bisector: $E = \frac{1}{4 \pi \varepsilon_0} \frac{p}{r^3}$
• Torque: $\tau = p E \sin \theta$
  • Dipole aligns with external E field.

• Magnetic field:
  • Moving charge produces B field.
  • Unit: Tesla (T), 1 T = 1 N·s/m·C; 1 T = 10⁴ gauss
• Magnetic materials:
  • Diamagnetic: no unpaired e-, weakly repelled (wood, water)
  • Paramagnetic: unpaired e-, weakly attracted (Al, Cu, Au)
  • Ferromagnetic: unpaired e-, strongly attracted (Fe, Ni, Co)
• Field lines:
  • Bar magnets: N→S, circular; monopoles impossible.
• Magnetic fields from current:
  • Long straight wire: $B = \frac{\mu_0 I}{2 \pi r}$
  • µ₀ = 4π × 10⁻⁷ T·m/A
  • Right-hand rule: thumb = current, fingers = B direction
  • Circular loop: $B = \frac{\mu_0 I}{2 r}$ at center
• Magnetic force:
  • On moving charge: $F_B = q v B \sin \theta$
  • Right-hand rule for direction: thumb = velocity, fingers = B, palm = + charge force
  • Uniform circular motion: $F_B = F_C = \frac{mv^2}{r}$
• Current-carrying wire:
  • $F_B = I L B \sin \theta$
  • L = wire length, I = current
  • Direction via right-hand rule
  • Example: 2 m wire, I = 5 A, B = 30 gauss → $F_B = I L B \sin 90° = 3 × 10^{-2}\ \mathrm{N}$