Static Electric and Magnetic Fields With easy examples.

Electrostatics is the study of electric charges at rest and the forces and fields they create; magnetostatics is the study of steady electric currents and the magnetic fields around them. A balloon sticking to a wall is electrostatics; the field around a current-carrying wire is magnetostatics. Together they are the foundation of everything from capacitors to motors.

These static fields matter because nearly every electrical device is a controlled arrangement of them. Capacitors store energy in electric fields, motors work through magnetic fields, and insulation is designed by mapping field concentrations. The same few laws predict all of it, and they repay learning once and using forever.

Key Concepts

• Electric field E (V/m): the force per unit charge; field lines start on positive charges and end on negative ones, and never cross.
• Electric flux density D = ε × E; permittivity ε0 = 8.854 × 10⁻¹² F/m sets the scale in free space.
• Electric potential V (volts): potential energy per unit charge; E points from high potential toward low potential.
• Magnetic flux density B (tesla): field lines form closed loops with no beginning or end — there are no magnetic charges.
• Magnetic field strength H = B/µ (At/m); permeability µ0 = 4π × 10⁻⁷ H/m in free space.
• Superposition: fields from multiple sources add vectorially at every point.

Formulas

• Coulomb's law: F = k × q1 × q2 / r², with k = 9 × 10⁹ N·m²/C²; like charges repel, unlike charges attract.
• Field of a point charge: E = k × Q / r², directed radially outward.
• Gauss's law: total electric flux through a closed surface = Qenclosed / ε0.
• Potential of a point charge: V = k × Q / r.
• Field around a long straight wire: B = µ0 × I / (2π × r), circling the wire by the right-hand rule.
• Force on a moving charge: F = q × v × B, maximum when the motion is perpendicular to B.
• Solenoid field: B = µ0 × N × I / l.

Worked Example

1. Two 1 µC charges sit 10 cm apart in air. F = 9 × 10⁹ × (10⁻⁶ × 10⁻⁶) / (0.1)².
2. That gives F = 0.9 N — about the weight of a small apple, from charges you cannot even see.
3. The E field 10 cm from one charge: E = 9 × 10⁵ V/m = 900 kV/m — near air's breakdown (~3 MV/m), which is why sharp conductors spark easily.
4. A 10 A wire: at 1 cm distance, B = (4π × 10⁻⁷ × 10)/(2π × 0.01) = 2 × 10⁻⁴ T = 200 µT — about four times Earth's field, easily visible on a compass.

Common Misconceptions

• "Electric field lines can cross." They cannot; a crossing would mean two different field directions at one point, which is impossible.
• "Magnetic field lines start at the north pole and end at the south." Outside the magnet they run north to south, but inside they continue south to north, forming closed loops — magnetism has no isolated poles.
• "Shielding works the same for both." Electric fields are blocked by any conductor, but magnetic shielding needs high-permeability mu-metal to divert the flux.

Real-World Applications

• Capacitor design and high-voltage insulation coordination.
• Inkjet printers and photocopiers using controlled static charge.
• Electric motors and generators built around B fields.
• MRI scanners using superconducting solenoids.

Two tiny charges push with nearly a newton; a modest current makes a field stronger than Earth's. Coulomb and Gauss map the electric side, Biot-Savart and Ampère the magnetic side — every electrical machine is assembled from these pieces.