Three concentric metallic spherical shells of | vedclass

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

Question

(B) Let the surface charge densities be $\sigma$. Since the surface charge densities on the outer surfaces are equal,we have:$\sigma = \frac{q_1}{4\pi

Vedclass · Accepted Answer

$1 : 3 : 5$

Vedclass · Answer

(B) Let the surface charge densities be $\sigma$. Since the surface charge densities on the outer surfaces are equal,we have:$\sigma = \frac{q_1}{4\pi R^2} = \frac{q_2}{4\pi (2R)^2} = \frac{q_3}{4\pi (3R)^2}$,where $q_1, q_2, q_3$ are the charges on the outer surfaces of the shells.From the property of induction,the charge on the outer surface of the first shell is $q_1 = Q_1$.The charge on the outer surface of the second shell is $q_2 = Q_1 + Q_2$.The charge on the outer surface of the third shell is $q_3 = Q_1 + Q_2 + Q_3$.Equating the densities: $\frac{Q_1}{R^2} = \frac{Q_1 + Q_2}{4R^2} = \frac{Q_1 + Q_2 + Q_3}{9R^2}$.From $\frac{Q_1}{1} = \frac{Q_1 + Q_2}{4}$,we get $4Q_1 = Q_1 + Q_2 \Rightarrow Q_2 = 3Q_1$.From $\frac{Q_1}{1} = \frac{Q_1 + Q_2 + Q_3}{9}$,we get $9Q_1 = Q_1 + (3Q_1) + Q_3 \Rightarrow 9Q_1 = 4Q_1 + Q_3 \Rightarrow Q_3 = 5Q_1$.Thus,the ratio $Q_1 : Q_2 : Q_3 = Q_1 : 3Q_1 : 5Q_1 = 1 : 3 : 5$.

Three concentric metallic spherical shells of radii $R, 2R, 3R$ are given charges $Q_1, Q_2, Q_3$ respectively. It is found that the surface charge densities on the outer surfaces of the shells are equal. Then,the ratio of the charges given to the shells,$Q_1 : Q_2 : Q_3$ is

Similar Questions

If the pair of straight lines $xy-x-y+1=0$ and the line $ax+2y-3a=0$ are concurrent,then $a$ is equal to

In a Young's double-slit experiment,the fringe width is $0.2 \, mm$. If the wavelength of light used is increased by $10\%$ and the separation between the slits is also increased by $10\%$,the fringe width will be.......$mm$.

Hypo is used in photography because of its

If the temperature of the sun were to increase from $T$ to $2T$ and its radius from $R$ to $2R$,then the ratio of the radiant energy received on Earth to what it was previously will be

Who first discovered lichens?

Vedclass Test Series

Exam Paper Generator

Online Exam Module