Electromagnetism Essentials: Fields, Capacitance, and Flux
Electric field from a point charge, parallel plate capacitance, magnetic flux, and resistivity — four foundational electromagnetism calculations.
Electric fields, capacitors, magnetic flux, and material resistivity are four of the most foundational calculations in an introductory electromagnetism course.
Electric field from a point charge
Field strength is E = k × |Q| / r², where k ≈ 8.99×10⁹ N·m²/C². A 1 microcoulomb charge measured 0.1m away produces a field of 899,000 N/C — field strength always points away from positive charges and toward negative ones.
Parallel plate capacitance: geometry determines storage capacity
Capacitance is C = ε₀ × A / d. Plates with 0.02 m² area spaced 1mm apart yield a capacitance of about 1.77×10⁻¹⁰ farads — larger plate area or a smaller gap both increase capacitance, since more charge can be stored for the same voltage.
Magnetic flux: field lines through a surface
Flux is Φ = B × A × cos(θ), where θ is the angle between the field and the surface's normal. A 0.5 T field through a 0.02 m² surface, aligned perpendicular (0°), gives a flux of 0.01 Wb — at 90°, flux drops to zero since no field lines actually pass through the surface at that angle.
Resistivity: reversing the wire resistance formula
Resistivity is ρ = R × A / L, calculated from a measured sample's resistance, area, and length. A 2Ω measurement across a 2×10⁻⁶ m² cross-section over 10m gives a resistivity of about 4×10⁻⁷ Ω·m — close to values for materials like iron or nichrome, distinct from copper's much lower 1.68×10⁻⁸ Ω·m.
Four pillars of electromagnetism
Fields, capacitance, flux, and resistivity together explain how charge, current, and materials interact. Try the electric field calculator, parallel plate capacitor calculator, magnetic flux calculator, and resistivity calculator.