ELECTROMAGNETISMElectromagnetismPhysics Calculator

Electric Field

The electric field E = F/q describes the force per unit charge. For a point charge: E = kQ/r². Field lines point away from positive charges, toward negative. Superposition applies for multiple charges.

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E = kQ/r² for point charge — inverse square law Parallel plates: uniform E = V/d Field lines point from + to − charge Force on charge: F = qE

Key quantities
E = kQ/r²
Point charge
Key relation
E = V/d
Parallel plates
Key relation
F = qE
Force
Key relation
8.99×10⁹ N⋅m²/C²
k
Key relation

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Why: Electric fields govern electrostatic forces, capacitor behavior, and electromagnetic phenomena. Field strength determines force on any charge placed in the field.

How: Coulomb's law: E = kQ/r² for point charges. Parallel plates: E = V/d (uniform). Superposition: add fields from multiple charges. Force F = qE on test charge q.

E = kQ/r² for point charge — inverse square lawParallel plates: uniform E = V/d

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Calculate Electric FieldEnter charge and geometry to compute field strength, force on test charge, and potential

⚡ Point Charge Field

Electric field from a point charge: 1 μC at 10 cm distance

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🔋 Parallel Plate Capacitor

Uniform field between parallel plates: 100V across 1mm gap

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📏 Infinite Line Charge

Field from infinite line charge: 5 nC/m at 5 cm distance

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🌐 Charged Sphere (Outside)

Field outside uniformly charged sphere: 10 μC, radius 2 cm, at 5 cm

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🧲 Electric Dipole Field

Field from electric dipole: moment 1×10⁻²⁹ C⋅m at 30° angle

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Geometry & Mode

Point Charge Parameters

For educational and informational purposes only. Verify with a qualified professional.

🔬 Physics Facts

Coulomb's constant k = 8.99×10⁹ N⋅m²/C² — from ε₀ and c

— NIST

📐

Parallel plate field E = V/d is uniform between plates

— HyperPhysics

🔋

Electric field has units N/C or V/m — equivalent dimensions

— Physics Classroom

📏

Field obeys superposition — total E is vector sum of contributions

— MIT OCW

🎯 Key Takeaways

  • • Electric field strength follows an inverse-square law for point charges (E ∝ 1/r²)
  • • Parallel plate capacitors create uniform electric fields (E = V/d)
  • • Coulomb's constant k = 8.99 × 10⁹ N⋅m²/C² governs all electrostatic interactions
  • • Electric field is a vector quantity with both magnitude and direction
  • • Superposition principle: fields from multiple charges add vectorially

💡 Did You Know? Facts

Lightning bolts create electric fields of about 3 million V/m — strong enough to ionize air molecules and create a visible plasma channelSource: NOAA
🧲Michael Faraday invented the concept of 'lines of force' in the 1830s — the precursor to our modern electric field conceptSource: Royal Institution
🔬The electric field inside a conductor is always zero at equilibrium — charges redistribute to cancel any internal fieldSource: MIT OpenCourseWare
💎The electric field at the surface of a proton is approximately 10²¹ V/m — trillions of times stronger than lightningSource: NIST
🌍Earth has a natural electric field of about 100 V/m pointing downward near the surface during fair weatherSource: NASA
🏥Defibrillators use electric fields of about 6,000 V/m across the heart to restore normal rhythmSource: American Heart Association

📖 How Electric Fields Work

An electric field is a region of space where a charged particle experiences a force. Electric fields are created by electric charges or by changing magnetic fields, and they are fundamental to electromagnetism.

Point Charges (Coulomb's Law)

For a point charge q, the field strength at distance r is E = kq/r². The field points radially outward from positive charges and inward toward negative charges. The inverse-square dependence means doubling the distance reduces the field to 1/4.

Parallel Plates

Two parallel conducting plates with voltage V and separation d create a uniform field E = V/d between them. This configuration is used in capacitors, particle accelerators, and electrostatic precipitators.

Line Charges

An infinite line charge with linear charge density λ creates a field E = λ/(2πε₀r) that decreases as 1/r — slower than the 1/r² of point charges. This geometry applies to charged wires and coaxial cables.

🎯 Expert Tips

💡 Use Gauss's Law for Symmetry

For highly symmetric charge distributions (spheres, cylinders, planes), Gauss's law is far easier than direct integration of Coulomb's law.

💡 Check Units Carefully

Electric field can be expressed as N/C or V/m — they're equivalent. Always convert charges to Coulombs and distances to meters before calculating.

💡 Superposition is Key

For multiple charges, calculate each field separately then add as vectors. Remember fields have direction — use components for non-collinear charges.

💡 Field Lines Tell the Story

Field lines start on positive charges and end on negative charges. Their density indicates field strength. They never cross each other.

⚖️ Comparison Table

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❓ FAQ Section

What is the difference between electric field and electric potential?

Electric field (E) is a vector quantity representing force per unit charge (N/C), while electric potential (V) is a scalar representing energy per unit charge (J/C). The field is the negative gradient of potential: E = -dV/dr.

Why does field strength decrease with distance?

For point charges, the field follows an inverse-square law (E ∝ 1/r²) because field lines spread over a spherical area (4πr²) that grows with distance squared. This is fundamental to 3D geometry.

What units is electric field measured in?

Electric field is measured in Newtons per Coulomb (N/C) or equivalently Volts per meter (V/m). Both units are identical: 1 N/C = 1 V/m.

Can electric fields exist in a vacuum?

Yes. Electric fields propagate through vacuum at the speed of light. They dont require a medium — this is why electromagnetic radiation can travel through space.

What is the strongest electric field possible?

The Schwinger limit (~1.3 × 10¹⁸ V/m) is the theoretical maximum where the field is strong enough to create electron-positron pairs from the vacuum via quantum electrodynamics.

How do conductors affect electric fields?

The electric field inside a perfect conductor is zero at equilibrium. Charges redistribute on the surface to cancel any internal field — this is the basis of Faraday cages and electrostatic shielding.

What is Coulombs constant and why is it important?

Coulombs constant k = 8.99 × 10⁹ N⋅m²/C² relates force, charge, and distance in electrostatics. It equals 1/(4πε₀) where ε₀ is the permittivity of free space.

How do I calculate the field from multiple charges?

Use superposition: calculate each charges field independently, then add them as vectors. For N charges, E_total = Σ(kqᵢ/rᵢ²)r̂ᵢ. This works because Maxwells equations are linear.

📊 Infographic Stats

8.99×10⁹
Coulomb's Constant (N⋅m²/C²)
1.6×10⁻¹⁹
Electron Charge (C)
3×10⁶
Air Breakdown (V/m)
100
Earth Surface Field (V/m)

⚠️ Disclaimer

This calculator provides theoretical electric field calculations based on idealized models. Real-world factors such as dielectric materials, conductor geometry, edge effects, and relativistic corrections may affect actual results. Always verify critical calculations with experimental data or professional simulation software.

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