Electromagnetism and Maxwell's Equations Quiz

Fields

• A scalar field is a function that assigns a numerical value to each point in space.
• A vector field is a function that assigns a vector to each point in space.

Vector Calculus Operations

• Gradient of a scalar field: a vector field that points in the direction of the maximum rate of increase of the scalar field.
• Divergence of a vector field: a scalar field that describes the rate of flux of the vector field.
• Curl of a vector field: a vector field that describes the rotation of the original vector field.

Maxwell's Equations

• Maxwell's First Equation (Gauss's Law for Electric Field): ∇ ⋅ E = ρ/ε₀, relates electric flux to charge distribution.
• Maxwell's Second Equation (Gauss's Law for Magnetic Field): ∇ ⋅ B = 0, states that magnetic charges do not exist.
• Maxwell's Third Equation (Faraday's Law of Induction): ∇ × E = -∂B/∂t, describes how changing magnetic fields induce electric fields.
• Maxwell's Fourth Equation (Ampere's Law with Maxwell's Correction): ∇ × B = μ₀J + μ₀ε₀∂E/∂t, relates magnetic fields to electric currents and displacement currents.

Electromagnetic Induction

• Electrostatics: the study of stationary electric charges and their effects.
• Magnetostatics: the study of stationary magnetic fields and their effects.
• Faraday's Law of Induction: describes how changing magnetic flux induces electric fields.
• Ampere's Law: relates magnetic fields to electric currents in static fields.
• Ampere's Law in Time-Varying Fields: includes the effect of displacement currents in time-varying fields.