Question

The radii of inner and outer spheres of a spherical capacitor are $8~\text{cm$ and $9~\text{cm}$ respectively. The outer sphere is earthed and the inner sphere is charged. If the space is filled with a dielectric constant $K = 5$, the capacitance is}

• A. $400~\text{pF}$
• B. $40~\text{pF}$
• C. $400~\mu\text{F}$
• D. $40~\mu\text{F}$

Hint:

Use spherical capacitor formula with dielectric: $C = 4\pi\varepsilon_0 K \cdot \dfrac{ab}{b-a}$.

Answer 1

The Correct Option is A

Capacitance of spherical capacitor: $C = 4\pi\varepsilon_0 K \cdot \dfrac{ab}{b-a}$
$a = 0.08~\text{m}, b = 0.09~\text{m}, K = 5$
$C = 4\pi \cdot 8.85 \times 10^{-12} \cdot 5 \cdot \dfrac{0.08 \cdot 0.09}{0.01}$
$= 4\pi \cdot 8.85 \times 10^{-12} \cdot 5 \cdot 0.72 = 400~\text{pF}$ (approx)