Electric Field (Point Charge)

📊 intermediate

$$E = k\frac{q}{r^2}$$

Electric field magnitude due to a point charge.

Variables & Units

$E$

Electric field magnitude

Unit: $\text{N/C}$ or $\text{V/m}$

$k$

Coulomb constant

Unit: $\text{N·m}^2/\text{C}^2$

$q$

Source charge

Unit: $\text{C}$

$r$

Distance from charge

Unit: $\text{m}$

Key Information

📐 Derived From

Coulomb's law: $E = F/q_0$

💡 Example

Charge $q=1\,\mu\text{C}$ at $r=0.1\,\text{m}$: $E = (8.99\times10^9)(1\times10^{-6})/(0.1)^2 = 8.99\times10^5\,\text{N/C}$.

🔧 Applications

Capacitor design, particle accelerators, lightning rods

⚠️ Constraints

Point charge, static field

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