Derive an expression for the capacitance of a parallel plate capacitor with (a)A dielectric slab (b)a metallic plate in between the plates of the capacitor
Answers
Let A be the plate area and d be the distance between the plates,
1) A dielectric slab of thickness t is inserted,
Due to polarization inside the dielectric electric field will reduce,
So outside of dielectric, field = E₀
inside of dielectric, field = E = E₀/k
where k is the dielectric constant,
So the net potential will be,
V = Et + E₀(d-t)
=> V = E₀t/k + E₀(d-t)
=> V = E₀(d - t + t/k)
we know that, E₀ = q/ε₀A
=> V = q(d - t + t/k)/ε₀A
=> C = q/V
=> C = ε₀A/(d - t + t/k)
which is the required expression for capacitance,
2) A metallic plate of thickness t is inserted,
when a conducting metallic plate is inserted then electric field inside the plate will be zero
=> E = E₀/k = 0
=> k = ∞
hence putting the value of k in the above equation we get,
C = ε₀A/(d - t)
which is the required expression for capacitance with metallic plate
Answer:
Let A be the plate area and d be the distance between the plates,
1) A dielectric slab of thickness t is inserted,
Due to polarization inside the dielectric electric field will reduce,
So outside of dielectric, field = E₀
inside of dielectric, field = E = E₀/k
where k is the dielectric constant,
So the net potential will be,
V = Et + E₀(d-t)
=> V = E₀t/k + E₀(d-t)
=> V = E₀(d - t + t/k)
we know that, E₀ = q/ε₀A
=> V = q(d - t + t/k)/ε₀A
=> C = q/V
=> C = ε₀A/(d - t + t/k)
which is the required expression for capacitance,
2) A metallic plate of thickness t is inserted,
when a conducting metallic plate is inserted then electric field inside the plate will be zero
=> E = E₀/k = 0
=> k = ∞
hence putting the value of k in the above equation we get,
C = ε₀A/(d - t)
which is the required expression for capacitance with metallic plate