Electric Field Calculator

The electric field is a vector quantity representing force per unit charge (N/C), while the electric potential is a scalar quantity representing energy per unit charge (V = J/C). They are related: the electric field points in the direction of decreasing potential, and E = −dV/dr for radial fields. The potential is often easier to compute because scalar addition is simpler than vector addition.

Use the principle of superposition: the total electric field at any point is the vector sum of the fields due to each individual charge. Calculate each field separately using E = kq/r², then add them as vectors, accounting for their directions. For continuous charge distributions, replace the sum with an integral over the charge distribution.

Electric field lines are visual representations of the electric field. They start on positive charges and end on negative charges (or extend to infinity). The density of field lines is proportional to the field strength, and the tangent to a field line at any point gives the field direction. Field lines never cross, because the field has a unique direction at each point.

The inverse-square dependence arises from the geometry of three-dimensional space. The field from a point charge spreads uniformly over a spherical surface of area 4πr². As the radius doubles, the same total flux passes through four times the area, so the field intensity drops by a factor of four. This is a consequence of Gauss's Law and the 1/r² behavior is common to all central force fields in 3D space.

The Earth's fair-weather atmospheric electric field is about 100 V/m pointing downward. Near a Van de Graaff generator, fields reach 10⁶ V/m. The dielectric breakdown of air occurs at approximately 3 × 10⁶ V/m, producing sparks or lightning. Inside atoms, fields at the electron orbit reach about 5 × 10¹¹ V/m, demonstrating the enormous strength of electromagnetic forces at the atomic scale.