From lightning during thunderstorms to electronic devices, the phenomenon of electromagnetism is all around us. The electromagnetic force is one of the four fundamental forces of nature. It has been known to humanity in various forms for thousands of years. For example, the ancient Greek philosopher Thales of Miletus recorded his experiments on static electricity using amber and fur in the sixth century BC.
The English physicist William Gilbert studied the phenomenon of static electricity in...

For a conductor in which all charges are at rest, the conductor's surface is equipotential. The electric field is always perpendicular to equipotential surfaces. Therefore, in a conductor with static charges, the electric field just outside the conductor is always perpendicular to the conductor's surface. Any tangential component of the electric field will cause charges to move inside the conductor, which will violate the electrostatic nature of the system. In an electrostatic...

Electroconvulsive therapy (ECT), or shock therapy, remains a critical biomedical intervention for severe, treatment-resistant depression. While its origins can be traced back to Hippocrates' observations that malaria-induced convulsions alleviated mental illness, modern ECT has evolved significantly from its earlier, more primitive applications. First introduced in 1938 by Ugo Cerletti and his colleagues, ECT involves inducing controlled seizures using electrical currents. In its early...

When an electric field passes from one homogeneous medium to another, crossing the boundary between the two mediums imparts a discontinuity in the electric field. This results in electrostatic boundary conditions that depend on the type of mediums the field propagates through.
Consider a case where both the mediums across a boundary are two different dielectric materials. Recall that the electric field and electric displacement are proportional and related through the material's...

Consider an external electric field propagating through a homogeneous medium. When the electric field crosses the surface boundary of the medium, it undergoes a discontinuity. The electric field can be resolved into normal and tangential components. The amount by which the field changes at any boundary is given by the difference between the field components above and below the surface boundary.
The surface integral of an electric field is given by Gauss's law in integral form and is related to...

Van de Graaff generators (or Van de Graaffs) are devices used to demonstrate high voltage due to static electricity that can also be used for research. Robert Van de Graaff first built one in 1931 (based on original suggestions by Lord Kelvin) for use in nuclear physics research.
Van de Graaff uses both smooth and pointed surfaces, conductors, and insulators to generate large static charges and, hence, large voltages. A substantial excess charge can be deposited on the sphere because it moves...