For electricity, energy W {electric energy}| is charge q times voltage V: W = q*V. Electric energy is in joules: W = F*s = (k * q * Q / s^2) * s = q * (k * Q / s) = q * (E / s) = q*V, where F is electric force, k is electric-force constant, Q is charge, E is electric field, and s is distance.
Electric charge causes potential energy {electric field}| that radiates in all directions. Electric fields can cancel each other, because charges can be positive or negative.
potential
Electric charges q Q make electric force F, which decreases with distance r squared: F = k * q * Q / r^2, where k is electric force constant. Electric-field strength intensity H changes with distance r from charge Q: H = F/q = k * Q / r^2, where k is electric-force constant. Electric field depends on material electric permittivity.
Different distances have different potential energies. Charge can move between two electric-field points, causing potential-energy-change potential difference. Electric-field energy change E is potential difference V times charge q: E = F*s = (k * q * Q / s^2) * s = q * (k * Q / s) = q*V. Potential-energy difference is work done by electric force as charge moves through distance.
examples: surface
Potential is equal all over large charged-object surfaces. Otherwise, electrons flow to lowest-potential location to equalize potential.
examples: plate
Electric field H above charged plates equals charge q divided by electric permittivity k: H = q/k.
examples: rod
Electric field H above long rods varies as reciprocal of distance d from rod: H = C * (1/d).
examples: point
Electric field H around point charges or spheres varies as reciprocal of square of distance r from center: H = k * Q / r^2.
examples: dipole
Electric field H around dipole varies as reciprocal of cube of distance d from dipole center: H = C * (1 / d^3).
For electricity, power P {electric power}| is current I times voltage V: P = dE / dt = V * dq / dt = V*I.
Pressure on crystals can cause voltage {piezoelectricity}|. Pressure polarizes crystals, such as quartz, mica, or lead zirconate titanate (PZT). Pressure changes polarized-material charge separation to make voltage. In reverse, applying electric field contracts crystals in field direction.
Tendency for charges to flow depends on electric energy per charge {voltage}| {potential difference}. Higher potential is positive and attracts negative charge. If two points have potential difference and path exists, charge flows from one point to the other.
energy
Because field is electric force F divided by charge q, voltage V is electric field H times distance ds moved in field direction: V = H * ds = (F/q) * ds = (F * ds) / q = W/q, where W is electric energy. Voltage is electric energy divided by charge.
field
Separating charges using work creates electric field, with voltage between charges. Batteries separate charges to create voltage. Electromagnetic induction creates voltage by separating charges. Voltage V equals area A times negative of field change dH divided by time change dt: V = A * -dH / dt. Voltage V equals negative of inductance I times current change di divided by time change dt: V = -I * di / dt.
Electric fields {wakefield} can pulse and so force electrons to accelerate.
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Date Modified: 2022.0225