Magnetic Fields

• Biot-Savart law: The magnetic field at a point is proportional to the current flowing through a wire and inversely proportional to the distance from the point to the wire.

• Ampere’s law: The magnetic field around a current-carrying wire is proportional to the current and the length of the wire.

• Gauss’s law for magnetism: There are no magnetic monopoles, and the net magnetic flux through any closed surface is zero.

• Magnetic dipole moment: The magnetic dipole moment of a current loop is proportional to the current and the area of the loop.

• Magnetic field due to a current-carrying wire: The magnetic field around a current-carrying wire is in the shape of a circle, with the direction of the field given by the right-hand rule.

• Magnetic field due to a solenoid: The magnetic field inside a solenoid is uniform and in the direction of the solenoid’s axis.

• Magnetic field due to a toroid: The magnetic field inside a toroid is uniform and in the direction of the toroid’s axis.

• Faraday’s law of electromagnetic induction: A changing magnetic field induces an electric field.

• Lenz’s law: The direction of the induced electric field is such that it opposes the change in magnetic flux.

EM Waves

• Maxwell’s equations: A set of four partial differential equations that describe the behavior of electric and magnetic fields.

• Wave equation: A partial differential equation that describes the propagation of waves.

• Plane waves: EM waves that have a constant amplitude and phase across a plane perpendicular to the direction of propagation.

• Spherical waves: EM waves that have a constant amplitude and phase across a sphere centered on the source.

• Poynting vector: A vector that represents the energy flux of an EM wave.

• Wave energy: The energy carried by an EM wave per unit time per unit area.

• Wave momentum: The momentum carried by an EM wave per unit time per unit area.

• Doppler effect: The change in frequency of an EM wave due to the relative motion of the source and observer.

• Reflection and refraction of EM waves: The change in direction of an EM wave when it encounters a boundary between two different media.

• Polarization of EM waves: The orientation of the electric field vector of an EM wave.