A spherical condenser has inner and outer sph | vedclass

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

Question

(C) When the outer sphere is earthed,the capacitance $C_1$ of the spherical capacitor is given by: $C_1 = 4\pi \varepsilon_0 \frac{ab}{b - a}$ When th

Vedclass · Accepted Answer

$4\pi \varepsilon_0 b$

Vedclass · Answer

(C) When the outer sphere is earthed,the capacitance $C_1$ of the spherical capacitor is given by: $C_1 = 4\pi \varepsilon_0 \frac{ab}{b - a}$ When the inner sphere is earthed,the outer sphere acts as an isolated conductor with capacitance $4\pi \varepsilon_0 b$ in parallel with the spherical capacitor. Thus,the total capacitance $C_2$ is: $C_2 = 4\pi \varepsilon_0 b + \frac{4\pi \varepsilon_0 ab}{b - a} = 4\pi \varepsilon_0 \left( \frac{b(b - a) + ab}{b - a} \right) = 4\pi \varepsilon_0 \left( \frac{b^2 - ab + ab}{b - a} \right) = 4\pi \varepsilon_0 \frac{b^2}{b - a}$ The difference in capacities is: $C_2 - C_1 = 4\pi \varepsilon_0 \left( \frac{b^2}{b - a} - \frac{ab}{b - a} \right) = 4\pi \varepsilon_0 \left( \frac{b^2 - ab}{b - a} \right) = 4\pi \varepsilon_0 \frac{b(b - a)}{b - a} = 4\pi \varepsilon_0 b$

$A$ spherical condenser has inner and outer spheres of radii $a$ and $b$ respectively. The space between the two is filled with air. The difference between the capacities of two condensers formed when the outer sphere is earthed and when the inner sphere is earthed will be:

Similar Questions

Eight drops of mercury, each of the same radius and having the same charge, coalesce to form a single larger drop. The capacitance of the larger drop compared to each individual smaller drop is how many times greater?

$1000$ small water drops,each of capacitance $C$,join together to form one large spherical drop. The capacitance of the bigger sphere is ......... $C$.

The stratosphere acts as a conducting layer for the Earth. If the stratosphere extends up to $50 \ km$ from the Earth's surface,calculate the capacitance of the spherical capacitor formed between the Earth's surface and the stratosphere in $F$. Take the radius of the Earth as $6400 \ km$.

The ratio of charge to potential of a body is known as

Sixty-four drops are joined together to form a bigger drop. If each small drop has a capacitance $C$,a potential $V$,and a charge $q$,then the capacitance of the bigger drop will be

Vedclass Test Series

Exam Paper Generator

Online Exam Module