Whether the field at a point is electric or magnetic depends, surprisingly, on your motion relative to the charges and currents. You’ll learn how to transform the fields measured in one reference frame to a second reference frame moving relative to the first.

《 LOOKING BACK Section 4.3 Relative motion

Electricity and magnetism can be summarized in four equations for the fields, called Maxwell’s equations, and one equation that tells us how charges respond to fields.

• Gauss’s law: Charges create electric fields.

• Gauss’s law for magnetism: There are no isolated magnetic poles.

• Faraday’s law: Electric fields can also be created by changing magnetic fields.

• Ampère-Maxwell law: Magnetic fields can be created either by currents or by changing magnetic fields.

《 LOOKING BACK Section 24.4 Gauss’s law

《 LOOKING BACK Section 29.6 Ampère’s law

《 LOOKING BACK Section 30.5 Faraday’s law

Maxwell’s equations predict the existence of self-sustaining oscillations of the electric and magnetic fields—electromagnetic waves—that travel through space without the presence of charges or currents.

• In a vacuum, all electromagnetic waves—from radio waves to x rays—travel with the same speed $v_{\text{em}}=1/\sqrt{{ϵ}_0{\mu }_0}=c$, the speed of light.

• The fields $\vec{E}$ and $\vec{B}$ are perpendicular to each other and to the direction of travel.

• Electromagnetic waves are launched by an oscillating dipole, called an antenna.

• Electromagnetic waves transfer energy.

• Electromagnetic waves also transfer momentum and exert radiation pressure.

《 LOOKING BACK Section 16.4 The wave equation

An electromagnetic wave is polarized if the electric field always oscillates in the same plane—the plane of polarization. Polarizers both create and analyze polarized light. You will learn to calculate the intensity of light transmitted through a polarizer and will see that light is completely blocked by crossed polarizers. Polarization is used in many types of modern optical instrumentation.