Physics · Electrostatic Potential And Capacitance · NEET
The energy is stored in the electric field itself, in the empty space between the plates — not in the charges on the plates. This is a key NCERT idea: energy density u = (1/2)ε₀E² exists wherever a field E exists. That is why the formula depends only on E, not on the charges directly. This view lets the same idea apply to light and radio waves, where fields carry energy through empty space.
Total energy U (in joules) is the whole energy stored in the capacitor: U = (1/2)CV² = (1/2)ε₀E²(Ad). Energy density u (in J/m³) is energy per unit volume: u = U / volume = (1/2)ε₀E². So u = U / (Ad). NEET may ask for either — read the units in the options. If options are in J, they want U; if in J/m³, they want u.
The 1/2 comes from the charging process. As you charge a capacitor, the voltage rises from 0 to its final value, so on average the work is done against half the final voltage. This is the same 1/2 that appears in (1/2)CV² and in spring energy (1/2)kx². It is not a units factor — it is real physics from building up the field from zero.
No. NCERT derives it using a parallel plate capacitor, but states clearly the result is very general. It holds for the field of any charge configuration — a point charge, a sphere, a dipole. Wherever the field strength is E, the energy density there is (1/2)ε₀E². For a point charge the field varies with distance, so u also varies with distance.
Replace ε₀ with ε = Kε₀, so u = (1/2)Kε₀E², where E is the field inside the dielectric and K is the dielectric constant. Be careful: inserting a dielectric usually reduces the field E (if charge is fixed), so you must use the reduced E value, not the original one. Always track which quantity (charge or voltage) is held constant before deciding how u changes.
A parallel plate capacitor has a uniform electric field 'E' in the space between the plates. If the distance between the plates is 'd' and the area of each plate is 'A', the energy stored in the capacitor is: (ε₀ = permittivity of free space)
Try the real previous-year questions from this chapter — each with the answer and a full solution.
u = (1/2)ε₀E², where ε₀ is the permittivity of free space and E is the electric field strength. Its SI unit is joule per cubic metre (J/m³).
Joule per cubic metre, J/m³. It equals energy divided by volume. You can verify: ε₀ has units C²/(N·m²) and E² has units (N/C)², so the product gives J/m³.
Total energy U = energy density u × volume of the field region. For a parallel plate capacitor, U = (1/2)ε₀E² × (A d), where A d is the volume between the plates.
Yes. Since E = σ/ε₀ between the plates, u = (1/2)ε₀E² = σ²/(2ε₀), where σ is the surface charge density. This form is useful in force-between-plates problems.
No. Where the field is stronger, energy density is higher (it depends on E²). Near a point charge the field is large, so u is large close to the charge and falls off rapidly with distance.
