Theory of electromagnetic fields
- Wolski, Andrzej
- arXiv:1111.4354CERN-2011-007PP.-15-65
 | Snapshot of a numerical solution to Maxwell's equations for a bunch of electrons moving through a beam position monitor in an accelerator vacuum chamber. The colours show the strength of the electric field. The bunch is moving from right to left: the location of the bunch corresponds to the large region of high field intensity towards the left hand side. (Image courtesy of M.\,Korostelev.) |
 | Electric field lines from a point charge $q$. The field lines are everywhere perpendicular to a spherical surface centered on the charge. |
 | Magnetic field lines around a long straight wire carrying a current $I$. |
 | Electric and magnetic fields in a plane electromagnetic wave in free space. The wave vector $\vec{k}$ is in the direction of the $+z$ axis. |
 | Electric and magnetic fields in a plane electromagnetic wave in a conductor. The wave vector is in the direction of the $+z$ axis. |
 | Integration over a distributed source. |
 | Hertzian dipole: the charges oscillate around the origin along the $z$ axis with infinitesimal amplitude. The vector potential at any point is parallel to the $z$ axis, and oscillates at the same frequency as the dipole, with a phase difference and amplitude depending on the distance from the origin. |
 | Distribution of radiation power from an Hertzian dipole. The current in the dipole is oriented along the $z$ axis. The distance of a point on the curve from the origin indicates the relative power density in the direction from the origin to the point on the curve. |
 | (a) Left: ``Pill box'' surface for derivation of the boundary conditions on the normal component of the magnetic flux density at the interface between two media. (b) Right: Geometry for derivation of the boundary conditions on the tangential component of the magnetic intensity at the interface between two media. |
 | (a) Left: ``Pill box'' surface for derivation of the boundary conditions on the normal component of the magnetic flux density at the interface between two media. (b) Right: Geometry for derivation of the boundary conditions on the tangential component of the magnetic intensity at the interface between two media. |
 | Incident, reflected, and transmitted waves on a boundary between two media. |
 | Electric and magnetic fields in the incident, reflected, and transmitted waves on a boundary between two media. Left: The incident wave is $N$ polarised, i.e. with the electric field normal to the plane of incidence. Right: The incident wave is $P$ polarised, i.e. with the electric field parallel to the plane of incidence. |
 | Electric and magnetic fields in the incident, reflected, and transmitted waves on a boundary between two media. Left: The incident wave is $N$ polarised, i.e. with the electric field normal to the plane of incidence. Right: The incident wave is $P$ polarised, i.e. with the electric field parallel to the plane of incidence. |
 | Rectangular cavity. |
 | Boundary conditions in a rectangular cavity. The field component $E_y$ is parallel to the walls of the cavity (and must therefore vanish) at $x = 0$ and $x = a_x$. |
 | Mode spectra in rectangular cavities. Top: all side lengths equal. Middle: two side lengths equal. Bottom: all side lengths different. Note that we show all modes, including those with two (or three) mode numbers equal to zero, even though such modes will have zero amplitude. |
 | Examples of modes in rectangular cavity. From top to bottom: (110), (111), (210), and (211). |
 | Examples of modes in rectangular cavity. From top to bottom: (110), (111), (210), and (211). |
 | Examples of modes in rectangular cavity. From top to bottom: (110), (111), (210), and (211). |
 | Examples of modes in rectangular cavity. From top to bottom: (110), (111), (210), and (211). |
 | Bessel functions. The red, green, blue and purple lines show (respectively) the first, second, third and fourth order Bessel functions $J_n(x)$. |
 | TE$_{110}$ mode in a cylindrical cavity. Left: Electric field. Right: Magnetic field. Top: 3-dimensional view. Bottom: Cross-sectional view. |
 | TE$_{110}$ mode in a cylindrical cavity. Left: Electric field. Right: Magnetic field. Top: 3-dimensional view. Bottom: Cross-sectional view. |
 | Fields in the TM$_{010}$ mode in a cylindrical cavity. Left: Electric field. Right: Magnetic field. |
 | Rectangular waveguide. |
 | Dispersion curve (in red) for waves in a waveguide. The broken black line shows phase velocity $\omega/k_z = c$. |
 | Group velocity in a waveguide. |
 | Inductance in a transmission line. |
 | Capacitance in a transmission line. |
 | Termination of a transmission line with an impedance $R$. |
 | A ``lossy'' transmission line. |
 | Coaxial cable transmission line. |
 | Inductance in a coaxial cable. A change in the current $I$ flowing in the cable will lead to a change in the magnetic flux through the shaded area; by Faraday's law, the change in flux will induce an electromotive force, which results in a difference between the voltages $V_2$ and $V_1$. |