Energy per unit volume for a capacitor having area A and separation d kept at potential difference V is given by:
A) (1/2) ε₀ V² / d²
B) (1/2 ε₀) V² / d²
C) (1/2) C^(1/2)
D) ε₀² / 2C
The energy stored in a capacitor is given by the formula:
U = (1/2) * C * V^2
Where:
U is the energy stored,
C is the capacitance,
V is the potential difference.
The capacitance (C) of a parallel plate capacitor is given by:
C = (ε₀ * A) / d
Where:
ε₀ is the permittivity of free space,
A is the area of the plates,
d is the separation between the plates.
Substitute the expression for C into the energy formula:
U = (1/2) * ((ε₀ * A) / d) * V^2
Now, this expression can be simplified:
U = (1/2) * ε₀ * A * V^2 / d
Therefore, the energy per unit volume (U/V) is:
U/V = (1/2) * ε₀ * A * V / d
The correct option is A. (1/2) * ε₀ * V^2 / d^2.
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