A spherical capacitor consists of two concentric spherical conductors. Find the capacitance of the spherical capacitor if the outer radius is 2 R and the inner radius is R.

Question

A spherical capacitor consists of two concentric spherical conductors. Find the capacitance of the spherical capacitor if the outer radius is 2 R and the inner radius is R. (A) 4 π ϵ0 R (B) 8 π ϵ0 R (C) (8 π ϵ0/ R ) (D) (4 π ϵ0/R)

Tardigrade Admin · Accepted Answer

Given, outer radius, b=2 R Inner radius, a=R As we know that, capacitance of spherical capacitor, C=4 π ε0((a b/b-a)) ∴ C=4 π ε0((R ⋅ 2 R/2 R-R))=4 π ε0 (2 R2/R) C=8 π ε0 R

Q. A spherical capacitor consists of two concentric spherical conductors. Find the capacitance of the spherical capacitor if the outer radius is $2 R$ and the inner radius is R.

$4 π ϵ_{0} R$

$8 π ϵ_{0} R$

$\frac{8 π ϵ _{0}}{R}$

$\frac{4 π ϵ _{0}}{R}$

Given, outer radius, $b = 2 R$
Inner radius, $a = R$
As we know that, capacitance of spherical capacitor,
$C = 4 π ε_{0} (\frac{ab}{b - a})$
$∴ C = 4 π ε_{0} (\frac{R \cdot 2 R}{2 R - R}) = 4 π ε_{0} \frac{2 R ^{2}}{R}$
$C = 8 π ε_{0} R$

Q. A spherical capacitor consists of two concentric spherical conductors. Find the capacitance of the spherical capacitor if the outer radius is 2R and the inner radius is R.

4πϵ0​R

8πϵ0​R

R8πϵ0​​

R4πϵ0​​