Maxwell Tension Supports the Water Bridge

TL;DR

This paper presents a theoretical explanation, based on Maxwell's pressure tensor, for how electric fields support water bridges, a phenomenon where water spans gaps between beakers without physical support.

Contribution

It introduces a quantitative theory explaining the forces that sustain water bridges using Maxwell's pressure tensor in dielectric fluids.

Findings

Electric fields enable stable water bridges.

Maxwell pressure tensor explains the supporting forces.

The theory aligns with experimental observations.

Abstract

A cylindrical flexible cable made up of pure fluid water can be experimentally spanned across a spatial gap with cable endpoints fixed to the top edges of two glass beakers. The cable has been called a water bridge in close analogy to iron cables employed to build ordinary span bridges. A necessary condition for the construction of a water bridge is that a large electric field exists parallel to and located within the water cable. Presently, there is no accepted detailed theory which quantitatively explains the forces which hold up the bridge. Our purpose is to present such theory based on the Maxwell pressure tensor induced by the electric field albeit within the condensed matter dielectric fluid cable.