Two spherical conductors of capacities 3 mu F | vedclass

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

Question

(C) We know that the capacitance of a spherical conductor is $C = 4 \pi \epsilon_0 r$. Since $C \propto r$,the ratio of capacitances is equal to the r

Vedclass · Accepted Answer

$\frac{2}{3}$

Vedclass · Answer

(C) We know that the capacitance of a spherical conductor is $C = 4 \pi \epsilon_0 r$. Since $C \propto r$,the ratio of capacitances is equal to the ratio of radii: $\frac{C_1}{C_2} = \frac{r_1}{r_2} = \frac{3}{2}$.Given that both spheres are at the same potential $V$,the charges are $Q_1 = C_1 V$ and $Q_2 = C_2 V$.The surface charge density is given by $\sigma = \frac{Q}{A} = \frac{Q}{4 \pi r^2}$.Substituting $Q = CV$,we get $\sigma = \frac{CV}{4 \pi r^2}$.Since $C = 4 \pi \epsilon_0 r$,we have $\sigma = \frac{(4 \pi \epsilon_0 r) V}{4 \pi r^2} = \frac{\epsilon_0 V}{r}$.Thus,$\sigma \propto \frac{1}{r}$.Therefore,$\frac{\sigma_1}{\sigma_2} = \frac{r_2}{r_1} = \frac{2 \ cm}{3 \ cm} = \frac{2}{3}$.

Two spherical conductors of capacities $3 \mu F$ and $2 \mu F$ are charged to the same potential,having radii $3 \ cm$ and $2 \ cm$ respectively. If $\sigma_1$ and $\sigma_2$ represent the surface charge density on the respective conductors,then $\frac{\sigma_1}{\sigma_2}$ is:

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 $......$

If the circumference of a sphere is $3 \ m$,then the capacitance of the sphere in water is (dielectric constant of water = $80$) (in $pF$)

Eight drops of mercury of equal radii possessing equal charges combine to form a big drop. Then the capacitance of the bigger drop compared to each individual small drop is ........ $\times$.

What is the capacitance of a spherical conductor with a radius of $1 \ m$?

The dimension of capacitance is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module