Electric Fields Concepts and Calculations

Electric Fields

• An electric field is a region surrounding a charged object where other charges experience a force.
• Electric field direction: away from positive charges and towards negative charges.
• Electric field strength (E) is proportional to the charge magnitude and inversely proportional to the distance squared from the charge.
• Formula: E = k * |q| / r²
  • E = electric field strength (N/C)
  • k = Coulomb's constant (8.99 × 10⁹ N·m²/C²)
  • q = charge (C)
  • r = distance from charge (m)
• Example: A +3 μC charge at 0.2 m has an electric field of 6.74 × 10⁶ N/C pointing outward.
• Electric field lines: show field direction, never intersect; closer lines indicate stronger field.
• Conductors allow free charge flow (metals); insulators do not (rubber, plastic).
• Gauss's Law: relates electric field around a closed surface to enclosed charge: ∮ E · dA = Q / ε₀
  • E = electric field
  • dA = differential area element
  • Q = enclosed charge
  • ε₀ = permittivity of free space (8.85 × 10⁻¹² C²/N·m²)

Oersted's Discovery

• Oersted (1820) discovered that electric current creates a magnetic field.
• Oersted's Experiment: A compass needle near a current-carrying wire deflected, direction depending on current: demonstrating electric current creates a magnetic field..
• Key takeaway: A moving charge (current) generates a magnetic field.
• Right-Hand Rule: Thumb in current direction, fingers curl in magnetic field direction.
• Magnetic Field of a Wire: Concentric circles around a long, straight wire; strength is directly proportional to current and inversely to distance from the wire.
• Formula for Magnetic Field around a Wire: B = (μ₀ * I) / (2 * π * r)
  • B = magnetic field strength (T)
  • μ₀ = permeability of free space (4π × 10⁻⁷ T·m/A)
  • I = current (A)
  • r = distance from wire (m)

Magnetic Fields and Forces

• A magnetic field is a region where a magnetic force can be detected; created by moving charges/permanent magnets. Field strength depends on distance and current.
• Magnetic field lines: point away from north pole and towards south pole, strongest where lines are closest.
• Current-carrying wire creates a magnetic field; strength depends on current and distance; direction determined by right-hand rule.
• Force on a moving charge in a magnetic field: F = qvB sin(θ)
  • F = force (N)
  • q = charge (C)
  • v = velocity (m/s)
  • B = magnetic field strength (T)
  • θ = angle between velocity and field
• Force on a current-carrying wire in a magnetic field: F = I * L * B * sin(θ)
  • I = current (A)
  • L = wire length (m)
  • B = magnetic field strength (T)
  • θ = angle between wire and field
• Example: A 0.5 m wire with 2 A current in a 0.3 T field (90°) experiences 0.3 N force.

Magnetic Fields and Forces in Practice

• Wire force in a magnetic field depends on current, length, and angle to the field; strongest when perpendicular.
• Example: A 3 A current in 0.8 m wire in a 0.2 T field (90°) experiences 0.48 N force.
• Solenoid: coil of wire; produces a strong, uniform magnetic field inside; field strength depends on turns of wire, current, and length.
• Formula for Magnetic Field inside a Solenoid: B = (μ₀ * N * I) / L
  • B = magnetic field (T)
  • μ₀ = permeability of free space (4π × 10⁻⁷ T·m/A)
  • N = number of turns of wire
  • I = current (A)
  • L = length of the solenoid (m)

Explore the fundamental concepts of electric fields, including their direction, strength, and behavior around charged objects. This quiz also covers important formulas like Gauss's Law and provides examples to test your understanding of electric fields.