Physics Chapter on Electricity and Magnetism

Ohm's Law

• Defines the relationship between voltage (V), current (I), and resistance (R).
• Formula: V = I × R
  • V: Voltage (Volts)
  • I: Current (Amperes)
  • R: Resistance (Ohms)
• Implications:
  • Current is directly proportional to voltage and inversely proportional to resistance.
  • Used to calculate the behavior of electrical circuits.

Electrostatics

• Study of electric charges at rest.
• Key concepts:
  • Coulomb's Law: Describes the force between two point charges.
    • Formula: F = k × (|q₁ × q₂|/r²)
      • F: Force (Newtons)
      • q₁, q₂: Point charges (Coulombs)
      • r: Distance between charges (meters)
      • k: Coulomb's constant (approximately 8.99 × 10⁹ Nm²/C²)
  • Electric Field (E): Region around a charged object where other charges experience force.
    • Formula: E = F/q (F: force, q: charge)
  • Potential Difference (Voltage): Work done per unit charge to move a charge from one point to another.

Magnetic Fields

• Produced by moving electric charges and magnetic dipoles.
• Characteristics:
  • Described by magnetic field lines, which indicate direction and strength.
  • Biot-Savart Law: Calculates the magnetic field generated by an electric current.
    • Formula: B = (μ₀/4π) × (I × dl × sin(θ)/r²)
      • B: Magnetic field (Tesla)
      • I: Current (Amperes)
      • dl: Infinitesimal length of the wire
      • θ: Angle between dl and r
      • r: Distance from the wire
  • Ampere's Law: Defines the relationship between magnetic field and electric current.
    • Formula: ∮B·dl = μ₀I_enc

Electromagnetic Induction

• The process of generating electric current from a changing magnetic field.
• Key principles:
  • Faraday's Law of Induction: The induced electromotive force (EMF) in a loop is proportional to the rate of change of magnetic flux through the loop.
    • Formula: EMF = -dΦ/dt (Φ: magnetic flux)
  • Lenz's Law: The direction of induced current opposes the change in magnetic flux that produced it.
• Applications:
  • Transformers, electric generators, and induction cooktops.

Ohm's Law

• Defines the relationship between voltage, current, and resistance.
• Formula: V = I × R, where V is voltage (Volts), I is current (Amperes), and R is resistance (Ohms).
• Key implication: Current is directly proportional to voltage and inversely proportional to resistance.
• Used to calculate electrical circuit behavior.

Electrostatics

• Study of stationary electric charges.
• Key concepts:
  • Coulomb's Law: Describes the force between two point charges.
    • Formula: F = k × (|q₁ × q₂|/r²), where F is the force (Newtons), q₁ and q₂ are the point charges (Coulombs), r is the distance between the charges (meters), and k is Coulomb's constant (approximately 8.99 × 10⁹ Nm²/C²).
  • Electric Field: Region around a charged object where other charges experience a force.
    • Formula: E = F/q, where E is electric field (N/C), F is force (N), and q is charge (C).
  • Potential Difference (Voltage): Work done per unit charge to move a charge from one point to another.

Magnetic Fields

• Produced by moving electric charges and magnetic dipoles.
• Key characteristics:
  • Described by magnetic field lines, which indicate the direction and strength of the field.
  • Biot-Savart Law: Calculates the magnetic field generated by an electric current.
    • Formula: B = (μ₀/4π) × (I × dl × sin(θ)/r²), where B is the magnetic field (Tesla), I is the current (Amperes), dl is an infinitesimal length of the wire, θ is the angle between dl and r, and r is the distance from the wire.
  • Ampere's Law: Defines the relationship between the magnetic field and electric current.
    • Formula: ∮B·dl = μ₀I_enc, where B is the magnetic field, dl is an infinitesimal length of the path of integration, and I_enc is the enclosed current.

Electromagnetic Induction

• Process of generating electric current from a changing magnetic field.
• Key principles:
  • Faraday's Law of Induction: The induced electromotive force (EMF) in a loop is proportional to the rate of change of magnetic flux through the loop.
    • Formula: EMF = -dΦ/dt, where Φ is the magnetic flux (Webers).
  • Lenz's Law: The direction of the induced current opposes the change in magnetic flux that produced it.
• Applications:
  • Transformers, electric generators, and induction cooktops.