Fields & Electromagnetism Formulas
Fields & Electromagnetism formulas cover Coulomb’s Law, Electric Field of a Point Charge, Electric Potential of a Point Charge and more. These calculators let you solve for any unknown by entering the values you already know. Use them for quick design checks, study, and verifying real circuits.
Fields & Electromagnetism Formula Calculators
- Coulomb’s Law F = k · q1 · q2 / r² Charge 1 100 nC, Charge 2 0.22 µC, Separation 1 mm → Force = 0.1977 kN
- Electric Field of a Point Charge E = k · q / r² Charge 100 nC, Distance 1 mm → Electric Field = 898.8 MV/m
- Electric Potential of a Point Charge V = k · q / r Charge 100 nC, Distance 1 mm → Potential = 898.8 kV
- Gauss’s Law (Electric Flux) ΦE = Qenc / ε0 Enclosed Charge 100 nC → Electric Flux = 11.29 kV·m
- Lorentz Magnetic Force F = q · v · B · sin(θ) Charge 100 pC, Velocity 10 mm/s, Flux Density 10 G, Angle v to B 1.5 ° → Force = 2.62 × 10⁻¹¹ µN
- Force on a Current-Carrying Wire F = B · I · L · sin(θ) Flux Density 10 G, Current 2 mA, Conductor Length 1 mm, Angle I to B 1.5 ° → Force = 5.24 × 10⁻⁵ µN
- Force Between Parallel Wires F/L = µ0 · I1 · I2 / (2π · d) Current 1 2 mA, Current 2 4.4 mA, Separation 0.1 mm → Force per Length = 0.0176 µN/m
- Magnetic Field of a Straight Wire B = µ0 · I / (2π · r) Current 2 mA, Distance 0.1 mm → Flux Density = 0.04 G
- Solenoid Magnetic Field B = µ0 · N · I / l Number of Turns 0.025, Current 2 mA, Solenoid Length 1 mm → Flux Density = 6.28 × 10⁻⁴ G
- Magnetic Dipole Moment m = N · I · A Number of Turns 0.025, Current 2 mA, Loop Area 10 mm² → Dipole Moment = 5 × 10⁻⁷ mA·m²
- Faraday’s Law of Induction emf = N · ΔΦ / Δt Number of Turns 0.025, Flux Change 100 µWb, Time Interval 100 µs → Induced EMF = 25 mV
- Motional EMF e = B · L · v Flux Density 10 G, Conductor Length 1 mm, Velocity 10 mm/s → Induced EMF = 10 nV
- Magnetic Field Energy Density u = B² / (2 · µ0) Flux Density 10 G → Energy Density = 0.3979 J/m³
- Hall Coefficient RH = 1 / (n · q) Carrier Density 1 × 10¹³ 1/cm³, Carrier Charge 100 µC → Hall Coefficient = 1 × 10⁻⁹ cm³/C
- Carrier Drift Velocity vd = I / (n · A · q) Current 2 mA, Carrier Density 1 × 10¹³ 1/cm³, Cross Section 0.1 mm², Carrier Charge 100 µC → Drift Velocity = 2 × 10⁻⁸ mm/s
- Cyclotron Frequency f = q · B / (2π · m) Charge 100 µC, Flux Density 10 G, Particle Mass 1 g → Frequency = 1.59 × 10⁻⁵ Hz
- Conductivity ↔ Resistivity σ = 1 / ρ Resistivity 1 nΩ·m → Conductivity = 1000 MS/m
- Number of Excess Electrons n = Q / e Charge 100 pC → Electron Count = 6.24 × 10⁸
Worked result for every Fields & Electromagnetism formula
| Formula | Expression | Worked result |
|---|---|---|
| Coulomb’s Law | F = k · q1 · q2 / r² | Charge 1 100 nC, Charge 2 0.22 µC, Separation 1 mm → Force = 0.1977 kN |
| Electric Field of a Point Charge | E = k · q / r² | Charge 100 nC, Distance 1 mm → Electric Field = 898.8 MV/m |
| Electric Potential of a Point Charge | V = k · q / r | Charge 100 nC, Distance 1 mm → Potential = 898.8 kV |
| Gauss’s Law (Electric Flux) | ΦE = Qenc / ε0 | Enclosed Charge 100 nC → Electric Flux = 11.29 kV·m |
| Lorentz Magnetic Force | F = q · v · B · sin(θ) | Charge 100 pC, Velocity 10 mm/s, Flux Density 10 G, Angle v to B 1.5 ° → Force = 2.62 × 10⁻¹¹ µN |
| Force on a Current-Carrying Wire | F = B · I · L · sin(θ) | Flux Density 10 G, Current 2 mA, Conductor Length 1 mm, Angle I to B 1.5 ° → Force = 5.24 × 10⁻⁵ µN |
| Force Between Parallel Wires | F/L = µ0 · I1 · I2 / (2π · d) | Current 1 2 mA, Current 2 4.4 mA, Separation 0.1 mm → Force per Length = 0.0176 µN/m |
| Magnetic Field of a Straight Wire | B = µ0 · I / (2π · r) | Current 2 mA, Distance 0.1 mm → Flux Density = 0.04 G |
| Solenoid Magnetic Field | B = µ0 · N · I / l | Number of Turns 0.025, Current 2 mA, Solenoid Length 1 mm → Flux Density = 6.28 × 10⁻⁴ G |
| Magnetic Dipole Moment | m = N · I · A | Number of Turns 0.025, Current 2 mA, Loop Area 10 mm² → Dipole Moment = 5 × 10⁻⁷ mA·m² |
| Faraday’s Law of Induction | emf = N · ΔΦ / Δt | Number of Turns 0.025, Flux Change 100 µWb, Time Interval 100 µs → Induced EMF = 25 mV |
| Motional EMF | e = B · L · v | Flux Density 10 G, Conductor Length 1 mm, Velocity 10 mm/s → Induced EMF = 10 nV |
| Magnetic Field Energy Density | u = B² / (2 · µ0) | Flux Density 10 G → Energy Density = 0.3979 J/m³ |
| Hall Coefficient | RH = 1 / (n · q) | Carrier Density 1 × 10¹³ 1/cm³, Carrier Charge 100 µC → Hall Coefficient = 1 × 10⁻⁹ cm³/C |
| Carrier Drift Velocity | vd = I / (n · A · q) | Current 2 mA, Carrier Density 1 × 10¹³ 1/cm³, Cross Section 0.1 mm², Carrier Charge 100 µC → Drift Velocity = 2 × 10⁻⁸ mm/s |
| Cyclotron Frequency | f = q · B / (2π · m) | Charge 100 µC, Flux Density 10 G, Particle Mass 1 g → Frequency = 1.59 × 10⁻⁵ Hz |
| Conductivity ↔ Resistivity | σ = 1 / ρ | Resistivity 1 nΩ·m → Conductivity = 1000 MS/m |
| Number of Excess Electrons | n = Q / e | Charge 100 pC → Electron Count = 6.24 × 10⁸ |
Variables used across Fields & Electromagnetism formulas
- F — Electrostatic force (N)
- q1, q2 — The two point charges (C)
- r — Separation between charges (m)
- kₑ — Coulomb constant 8.988×10⁹ N·m²/C²
- E — Electric field strength (V/m or N/C)
- q — Source charge (C)
- V — Electric potential (V)
- ΦE — Electric flux through the closed surface (V·m)
- Qenc — Net charge enclosed (C)
- ε₀ — Permittivity of free space 8.854×10⁻¹² F/m
- v — Speed of the charge (m/s)
- B — Magnetic flux density (T)
- θ — Angle between velocity and field (degrees)
- I — Current (A)
- L — Length of conductor in the field (m)
- F/L — Force per unit length (N/m)
- I1, I2 — Currents in the two wires (A)
- d — Separation between wires (m)
- N — Total number of turns
- l — Length of the solenoid (m)
- m — Magnetic dipole moment (A·m²)
- A — Area enclosed by the loop (m²)
- emf — Induced electromotive force (V)
- ΔΦ — Change in magnetic flux (Wb)
- Δt — Time over which the change occurs (s)
- e — Motional EMF (V)
- u — Magnetic energy density (J/m³)
- RH — Hall coefficient (m³/C)
- n — Charge-carrier density (1/m³)
- vd — Drift velocity (m/s)
- f — Cyclotron frequency (Hz)
- σ — Conductivity (S/m)
- ρ — Resistivity (Ω·m)
- Q — Total charge (C)
Questions people ask about Fields & Electromagnetism
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