Energy Stored in an Electric Field

⚡ Energy Stored in an Electric Field

Just as energy is stored in a magnetic field in inductors, energy is also stored in an electric field in capacitors. When a capacitor is charged, work is done to move electric charges against the electric field, and this energy is stored in the electric field between the plates.

🔋 Basic Concept

When a voltage V is applied across a capacitor of capacitance C, charge Q accumulates on the plates. This process stores energy in the electric field created between the plates.

⚡ Derivation of Energy Stored

Let’s derive the energy stored in a capacitor:

Q = charge on the plates
V = voltage across the plates
C = capacitance of the capacitor

The small work dW done in moving a small charge dq against the voltage v is:

$d W = v \cdot d q = \frac{q}{C} d q$

Integrating from q = 0 to q = Q:

W = \int_0^Q \frac{q}{C} dq = \frac{1}{C} \cdot \left[ \frac{q^2}{2} \right]_0^Q = \frac{Q^2}{2C}

✅ Final Formulas

The energy E stored in an electric field (capacitor) can be written in three equivalent forms:
E = (1/2) C V² = (1/2) QV = Q² / (2C)

🔄 Energy in Terms of Electric Field

For a parallel-plate capacitor:

Plate area = A
Plate separation = d
Permittivity = ε

Electric field E = V / d

The energy stored per unit volume (energy density) is:

u = (1/2) ε E² J/m³

🧠 Key Points

The energy is stored in the electric field between the plates.
Energy is recoverable when the capacitor is discharged.
Larger capacitance or voltage means more energy stored.
Used in power electronics, filters, camera flashes, defibrillators, etc.

Energy Stored in an Electric Field