Electric Charge Converter

Faraday's first law of electrolysis: m = (M × Q) / (n × F), where m is deposited mass, M is molar mass, Q is charge in Coulombs, n is valence (number of electrons per ion), and F = 96,485 C/mol. Example: to deposit 1 g of gold (M=197 g/mol, n=1): Q = 1 × 1 × 96485 / 197 = 490 C = 0.136 Ah ≈ 8.1 minutes at 1 A.

A typical lightning bolt transfers about 5 C in a total flash duration of ~200 ms, though the main return stroke carries most of this in about 0.2 ms (peak current ~30,000 A). Larger bolts can transfer 20-30 C. The potential difference is roughly 1-10 billion volts, making total energy about 1-5 GJ × 5 C = 5-25 GJ... but the actual released energy is only about 1-5 GJ, as most potential energy remains in the cloud.

Q = CV, where C is capacitance in Farads and V is voltage. A 100 μF capacitor at 400 V (in a camera flash circuit): Q = 100 × 10⁻⁶ × 400 = 0.04 C = 40 mC, storing energy E = ½CV² = ½ × 100×10⁻⁶ × 400² = 8 J. The human body has capacitance of about 100 pF — at 10,000 V static charge: Q = 1 μC, energy = 5 mJ — enough to cause a painful spark and damage sensitive electronics.

In quantum field theory, charge quantization follows from gauge symmetry: the U(1) gauge symmetry of electromagnetism requires that all particles couple to the photon field with integer multiples of a fundamental charge unit e. The quarks' fractional charges (e/3, 2e/3) are still integer multiples of e/3 — and since quarks are always confined in groups that total to integer multiples of e, all observed particles have integer charge.

Charge density can be linear (C/m), surface (C/m²), or volumetric (C/m³). Human nerve axon surface charge density: ~0.01 C/m². Earth's surface charge: about −1 nC/m² (total ~−600,000 C). Atomic nuclei: nuclear charge density ~10²⁴ C/m³. Charge density is measured via electric displacement field D = ε₀E + P, where P is polarization, using electrostatic probes or optical methods.

e/me = 1.602176634 × 10⁻¹⁹ C / 9.1093837015 × 10⁻³¹ kg = 1.75882 × 10¹¹ C/kg. This ratio, first measured by J.J. Thomson in 1897 using cathode rays in magnetic and electric fields, was the first indication of the electron as a discrete particle. The proton's charge-to-mass ratio is e/mp = 9.578 × 10⁷ C/kg — about 1836 times smaller.

Battery capacity in Ah measures the total charge deliverable: Q = I × t. A 3000 mAh battery can deliver: 3 A for 1 hour, or 1 A for 3 hours, or 0.1 A for 30 hours (approximately — real batteries have lower capacity at higher discharge rates, described by Peukert's law: C_actual = C_rated × (I_rated/I)^k, with k ≈ 1.1-1.3 for lithium-ion batteries).

Maxwell added the displacement current ∂D/∂t to Ampere's law to make it consistent with charge conservation: ∇ × H = J + ∂D/∂t. In a capacitor being charged, no actual current flows through the gap, but the changing electric field (displacement field) creates a magnetic field just as a real current would. This addition predicted electromagnetic waves and is fundamental to understanding how light propagates without a medium.

Yes. Electrons carry charge −e = −1.602 × 10⁻¹⁹ C. The sign of charge is a physical reality, not just a convention. Negative charges are attracted to positive and repelled by negative. In semiconductors, 'holes' (absence of electrons in the valence band) act as positive charge carriers. In plasmas, electrons and ions are separate charge carriers. Antimatter particles have opposite charge to their matter counterparts: the positron has charge +e, not −e.