Chapter 12: Electrostatics

The force between two point charges is directly proportional to the product of magnitudes of charges and inversely proportional to the square of distance between them.

• Formula: F = k * (q1 * q2) / r^2
• Electrostatic Constant (k): k = 1 / (4 * pi * epsilon_0) = 9 * 10^9 N m^2 C^-2.
• Vector Form: F_12 = -F_21 (Newton's 3rd Law).
• Effect of Medium: Dielectric reduces force by a factor of epsilon_r (Relative Permittivity). F_med = F_vac / epsilon_r.

Electric Field: Space around a charge where it exerts force.

• Electric Intensity (E): Force per unit charge. E = F / q. Unit: N/C or V/m.
• Field Lines: Imaginary lines showing direction of force. Start from +ve, end on -ve. Tangent gives direction. Closer lines = stronger field. No two lines cross.
• Applications:
  • Xerography (Photocopier): Selenium drum (photoconductor). Positive charge image formed, toner (negatively charged) sticks, transferred to paper, fused by heat.
  • Inkjet Printer: Charged ink droplets deflected by plates into gutter; uncharged droplets hit paper to form characters.

Electric Flux (Phi): Number of field lines passing through an area. Phi = E.A = EA cos(theta).

Gauss's Law: Total flux through a closed surface is 1/epsilon_0 times the total charge enclosed. Phi = Q / epsilon_0.

• Applications:
  1. Inside Hollow Sphere: Charge is on surface, Q_enc = 0 inside. Thus E = 0 (Shielding).
  2. Infinite Sheet of Charge: E = sigma / (2 * epsilon_0). (sigma = Surface charge density).
  3. Between Oppositely Charged Plates: E = sigma / epsilon_0.

Electric Potential (V): Work done in bringing a unit positive charge from infinity to a point. Unit: Volt (J/C).

• Potential Difference: Delta V = -E * d (E as Potential Gradient: E = -dV/dr).
• Potential due to Point Charge: V = (1 / 4 * pi * epsilon_0) * (q / r).
• Electron Volt (eV): Energy acquired by electron moving through 1V potential diff. 1 eV = 1.6 * 10^-19 J.

Technique to measure charge on electron.

• Principle: Balancing gravitational force (mg) with electric force (qE). q = mgd / V.
• Terminal Velocity: Used to find mass/radius of droplet. mg = 6 * pi * eta * r * v_t (Stokes' Law).
• Result: Charge is quantized. q = n * e. e = 1.6 * 10^-19 C.

Device to store charge. Q = CV.

• Parallel Plate Capacitor: C = A * epsilon_0 / d (Vacuum). C_med = A * epsilon_0 * epsilon_r / d (Dielectic). Dielectric increases capacitance.
• Electric Polarization: Dielectric molecules become dipoles in field, reducing effective E field.
• Energy Stored: U = 1/2 CV^2 = 1/2 Q^2/C = 1/2 QV.
• Charging/Discharging: Exponential process. Time Constant (RC): Time to reach 63% charge or discharge to 37%.