Consider a parallel plate capacitor of area A (of each plate) and separation ' d ' between the plates. If E is the electric field and ε₀ is the permittivity of free space between the plates, then potential energy stored in the capacitor is

Solution

Physics sir · 3 steps

Energy density times volume: 1/2ε₀ E² per unit volume, filling a box of volume Ad.

1. Start from the capacitor. The stored energy is U = 1/2CV². For a parallel plate capacitor, C = (ε₀ A)/d, and the uniform field gives V = Ed.

   U = 1/2((ε₀ A)/d)(Ed)² = 1/2ε₀ E² A d

2. Check with energy density. An electric field stores energy u = 1/2ε₀ E² per unit volume. The field fills the space between the plates, of volume Ad, so U = uAd, the same result.
3. So. The stored energy is 1/2ε₀ E² Ad, which is option (d).

The idea to keep. Energy in a field lives in the space itself: u = 1/2ε₀ E². Multiply by the volume the field fills and you have the stored energy, no matter how the question dresses it up.

Answer from the NTA final answer key. Solution by PrepWiser.