The Earth is assumed to be a charged conducti | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Assuming the Earth is a solid sphere of radius $R$. The volume of the sphere is $V = \frac{4}{3} \pi R^{3}$. The surface area of the sphere is $A

Vedclass · Accepted Answer

$12 \pi \epsilon_{0} \frac{V}{A}$

Vedclass · Answer

(A) Assuming the Earth is a solid sphere of radius $R$. The volume of the sphere is $V = \frac{4}{3} \pi R^{3}$. The surface area of the sphere is $A = 4 \pi R^{2}$. Dividing the volume by the surface area,we get: $\frac{V}{A} = \frac{\frac{4}{3} \pi R^{3}}{4 \pi R^{2}} = \frac{R}{3}$. From this,we find the radius $R = 3 \frac{V}{A}$. The capacitance $C$ of an isolated spherical conductor is given by $C = 4 \pi \epsilon_{0} R$. Substituting the value of $R$,we get: $C = 4 \pi \epsilon_{0} \left( 3 \frac{V}{A} \right) = 12 \pi \epsilon_{0} \frac{V}{A}$.

The Earth is assumed to be a charged conducting sphere having volume $V$ and surface area $A$. The capacitance of the Earth in free space is ($\epsilon_{0} =$ permittivity of free space).

Similar Questions

$A$ capacitor of capacitance $C$ is charged to a potential $V$. The flux of the electric field through a closed surface enclosing the positive plate of the capacitor is $......$

The capacitance of a spherical condenser is $1\,\mu F$. If the spacing between the two spheres is $1\,mm$,then the radius of the outer sphere is

If the energy stored in a spherical conductor having a charge of $12 \mu C$ is $6 \ J$,then the radius of the spherical conductor is (in $cm$)

The electric field between the two spheres of a charged spherical capacitor:

Two spherical conductors $A$ and $B$ of radii $a$ and $b$ $(b > a)$ are placed in air concentrically. $B$ is given a charge $+Q$ and $A$ is grounded. The equivalent capacitance of this system is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module