Question

Part A

Answer 1

Answer:

A) U₀ = ϵ₀AV²/2d

B) U₁ = (ϵ₀AV²)/6d

This means that the new energy of the capacitor is (1/3) of the initial energy before the increased separation.

C) U₂ = (kϵ₀AV²)/2d

Explanation:

A) The energy stored in a capacitor is given by (1/2) (CV²)

Energy in the capacitor initially

U₀ = CV²/2

V = voltage across the plates of the capacitor

C = capacitance of the capacitor

But the capacitance of a capacitor depends on the geometry of the capacitor is given by

C = ϵA/d

ϵ = Absolute permissivity of the dielectric material

ϵ = kϵ₀

where k = dielectric constant

ϵ₀ = permissivity of free space/air/vacuum

A = Cross sectional Area of the capacitor

d = separation between the capacitor

If air/vacuum/free space are the dielectric constants,

So, k = 1 and ϵ = ϵ₀

U₀ = CV²/2

Substituting for C

U₀ = ϵ₀AV²/2d

B) Now, for U₁, the new distance between plates, d₁ = 3d

U₁ = ϵ₀AV²/2d₁

U₁ = ϵ₀AV²/(2(3d))

U₁ = (ϵ₀AV²)/6d

This means that the new energy of the capacitor is (1/3) of the initial energy before the increased separation.

C) U₂ = CV²/2

Substituting for C

U₂ = ϵAV²/2d

The dielectric material has a dielectric constant of k

ϵ = kϵ₀

U₂ = (kϵ₀AV²)/2d