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...

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 permittivity....

Ligand-gated ion channels are transmembrane proteins that play a vital role in intercellular communication and functions of the nervous system. They allow the influx of ions across the membrane once the neurotransmitter binds, allowing the subsequent transmission of electrical excitation across the neurons. Other ligand-gated ion channels, like the γ-aminobutyric acid (GABA) receptor, permit anions like chloride into the cells on the binding of the GABA molecule. Their entry into the cell...

Underflow gates are vital for controlling water flow in irrigation canals. The three main types of underflow gates — vertical, radial, and drum gates — serve different purposes while ensuring effective flow management. Vertical gates move up and down, generating a free-flowing water jet; radial gates pivot to regulate the flow; and drum gates rotate for precise adjustments. The flow through these gates is influenced by downstream conditions, resulting in free or drowned outflow.Free and...

Ion channels are specialized proteins on the plasma membrane that allow charged ions to pass down their electrochemical gradient. Their main function is to maintain the membrane potential which is critical for cell viability. These channels are either gated or non-gated and can transport more than a thousand ions within milliseconds for the cellular event to occur.
Compared to the gated ion channels, the non-gated channels, also known as leakage or passive channels, have no gating mechanism....

Mechanically-gated ion channels are proteins found in eukaryotic and prokaryotic cell membranes that open in response to mechanical stress. Tension, compression, swelling, and shear stress can alter the conformation of the protein, opening a transmembrane channel that allows the passage of ions for signal transmission. In eukaryotes, mechanically-gated channels are distributed in several regions like the neurons, lungs, skin, bladder, and heart, where they play critical roles in numerous...