Test: Effect of Dielectric on Capacitance & Van De Graff Generator (November 19) - NEET MCQ

The material suitable for using as a dielectric must have high dielectric strength X and large dielectric constant K.

Here C₁ = ε₀A/d = 10pF …….(i)
(∵ K = 4)
= 8 × 10 (using (i)) 
= 80 pF

Capacitance of a parallel capacitor with air is C = ε₀A/d​
Capacitance of a same parallel plate capacitor with the introduction of a dielectric medium is C ′ = Kε₀A/d​
where K is the dielectric constant of a medium
or C′/C ​= K or K = 15/3​ = 5 or K = ε₀/ε ​
or ε = Kε₀ ​= 5 × 8.854 × 10⁻¹² = 0.44 × 10⁻¹⁰C²N ⁻¹ m⁻²

As capacitance C₀ = ε₀A/d
∴ after inserting copper plate C = ε₀A/d−b

as Q = cv
initially c = 5μF, v = 1v
∴ Q = 5 × 10^–6 c = 5μc
when dielectric is introduced, let capacitance be c'
∴ c' = [(A∈₀)/{d – t + (t/k)}]
here k = 4, t = 4 cm, d = 6 cm
∴ c' = [{(A∈₀)/d}/{{d – t + (t/k)}/d}] ------ dividing by d
As [(A∈₀)/d] = initially capacitance = c = 5μF
∴ c' = [c/{{6 – 4 + (4/4)}/6}] = [c/(3/6)] = 2c = 10μF
∴ Q' = c'v = 10 × 10^–6 × 1 = 10μc
∴ addition charge flowing = Q' – Q = 10 – 5 = 5μc

Van de Graff generator- is an electrostatic generator which is devised to produce very high voltage by means of an endless belt collecting electrostatic charge from a source and transferring it to a large isolated metal sphere on which a large change accumulates.

Van de Graff generator- is an electrostatic generator which is devised to produce very high voltage by means of an endless belt collecting electrostatic charge from a source and transferring it to a large isolated metal sphere on which a large change accumulates.

The Italian physicist, professor at Pavia, Count Alessandro Volta established that the animal electricity observed by Luigi Galvani in experiments with frog muscle tissue placed in contact with dissimilar metals, was not due to any exceptional property of animal tissues but was also generated whenever any wet body was sandwitched between dissimilar metals.

Although air is normally an insulator but at a sufficient high voltage, it ionises and become partially conducting.
The electric field at which it occurs is called breakdown field of air and is nearly equal to 3 × 10⁶V/m^-1

Here, V = 15 × 10⁶ V, dielectric strength
= 5 x 10⁷ V m-¹
Maximum electric field, E = 10% of dielectric strength

As E = V/r

= 3 m