Electric Field Calculator

Electric Field

The electric field is a vector quantity that describes the force per unit charge at any point in space:

E = F / q

For a point charge:

E = k × Q / r²

Where k = 8.99 × 10⁹ N⋅m²/C² (Coulomb's constant) or k = 1/(4πε₀)

• Field points away from positive charges
• Field points toward negative charges
• Units: N/C (newtons per coulomb) or V/m (volts per meter)

Coulomb's Law

The force between two point charges:

F = k × |Q₁ × Q₂| / r²

• Like charges repel (both positive or both negative)
• Unlike charges attract (one positive, one negative)
• Force follows inverse square law (double distance → 1/4 force)

Electric Potential

Electric potential (voltage) is the electric potential energy per unit charge:

V = k × Q / r

Potential energy of a charge q at potential V:

U = q × V

• Units: Volts (V) = Joules/Coulomb (J/C)
• Electron volt (eV): energy gained by electron moving through 1V
• Potential decreases with distance (1/r, not 1/r²)

Uniform Electric Field

Between parallel plates with voltage V and separation d:

E = V / d

• Field is constant (same magnitude everywhere)
• Used in capacitors, CRT displays, particle accelerators
• Force on charge: F = qE (constant throughout)

Real-World Applications

• Capacitors: Store energy in uniform electric fields
• Lightning: Buildup of charge creates enormous electric fields
• Atoms: Electrons bound to nucleus by electric force
• CRT Displays: Electrons steered by electric fields
• Van de Graaff Generator: Creates high voltages (millions of volts)
• Photocopiers: Use static electricity to transfer toner

Important Constants

• k (Coulomb's constant): 8.99 × 10⁹ N⋅m²/C²
• ε₀ (permittivity): 8.85 × 10⁻¹² C²/(N⋅m²)
• e (elementary charge): 1.602 × 10⁻¹⁹ C
• Electron mass: 9.109 × 10⁻³¹ kg

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