VoltOne

VoltOne is a calculator and reference for classical electrodynamics: nineteen modules, from electrostatics through radiation to the Lorentz transformation of fields. Every screen shows the relation it evaluates, the inputs it took, and the branch it is on. EVERY SCREEN SHOWS ITS GEOMETRY Seventeen screens draw the configuration you are in, and it follows your numbers: where r is measured from, which radius is the inner one, whether an angle opens from the normal or the surface, whether the acceleration lies along the velocity or across it. Those are the mistakes that produce a confident wrong answer. The two screens with no geometry say so instead. ELECTROSTATICS Fields and potentials of point-charge configurations. Gauss's law in closed form for line, plane, spherical shell, uniform sphere and cylinder, inside and outside. Multipole expansion, with the truncated potential shown against the exact one so you can see where it stops being useful. Method of images for a grounded plane and sphere. Capacitance and stored energy. Linear dielectrics, bound charge, and D against E made explicit rather than assumed. MAGNETOSTATICS Biot-Savart in closed form: straight segments, loops on and off axis, solenoids, Helmholtz pairs. Symmetric solutions of Ampere's law with the regions separated. Self and mutual inductance, and the stored magnetic energy. Linear magnetic media, including diamagnetic susceptibilities, which are negative by definition and are taken as ordinary input rather than rejected. WAVES Plane waves: polarisation, energy density, the Poynting vector, radiation pressure. Propagation in an ohmic conductor - complex wave number, attenuation and skin depth, with the good-conductor approximation and the full expression offered separately rather than silently substituted. Rectangular waveguide cutoff, phase and group velocity. Reflection and transmission at an interface, both polarisations, Brewster's angle and total internal reflection. The Lorentz oscillator model of dispersion. RADIATION AND RELATIVITY Electric and magnetic dipole radiation, with angular distributions. Radiation from a moving point charge, where acceleration along the velocity and across it are a choice you make, not a default you inherit. Lorentz transformation of E and B between inertial frames. TWO SYSTEMS OF UNITS Every quantity can be read in SI or Gaussian. The computation is always in SI and only the displayed numbers convert, so switching never changes a physical result. Quantities whose definition genuinely differs between the two systems are flagged, not presented as a simple rescaling. WHAT VERIFICATION HERE MEANS The relations are covered by 563 automated tests, and what those tests are is worth saying, because it is not the usual arrangement. The material this app is built from is symbolic: it develops the theory and prints almost no worked numerical examples, so there is no table of published answers to check against, and this app does not claim one. Each relation is instead checked against its own structure - limiting cases, symmetry, conservation and orthogonality identities, agreement between independently derived forms, and round-trips through the unit conversion. Where two treatments both cover a result, they are cross-checked. That is strong against algebraic, sign and transcription errors. It cannot prove a relation was read correctly off the page to begin with, and that limit is stated here rather than left for you to find. SCOPE Linear, isotropic, homogeneous media. Closed-form and series solutions only: no numerical field solver, no meshing, no finite elements. No material property tables. This is classical electrodynamics; quantum electrodynamics is out of scope. Not qualified for safety or certification decisions without independent verification. PRIVATE AND OFFLINE No account, no analytics, no network access at all. Everything runs on your device. You choose what to export. One purchase covers Mac and iPad.