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  • Three concentric spherical metallic shells X, Y and Z of radius a, b and c respectively [a < b < c] have surface charge densities <img alt="\sigma,-\sigma" src="https://entrancecorner.on

Three concentric spherical metallic shells X, Y and Z of radius a, b and c respectively [a < b < c] have surface charge densities \sigma,-\sigmaand \sigma, respectively. The shells X and Z are at same potential. If the radii of X & Y are 2 cm and 3 cm, respectively. The radius of shell Z is __________ cm.

Option: 1

5


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

\begin{aligned} & \mathrm{q}_{\mathrm{x}}=\sigma 4 \pi \mathrm{a}^2 \\ & \mathrm{q}_{\mathrm{y}}=-\sigma 4 \pi \mathrm{b}^2 \\ & \mathrm{q}_{\mathrm{z}}=\sigma 4 \pi \mathrm{c}^2 \end{aligned}
Potential of y
\begin{aligned} & \frac{\mathrm{q}_{\mathrm{x}}}{4 \pi \varepsilon_0 \mathrm{a}}+\frac{\mathrm{q}_{\mathrm{y}}}{4 \pi \varepsilon_0 \mathrm{~b}}+\frac{\mathrm{q}_{\mathrm{z}}}{4 \pi \varepsilon_0 \mathrm{c}}=\frac{\mathrm{q}_{\mathrm{x}}}{4 \pi \varepsilon_0 \mathrm{c}}+\frac{\mathrm{q}_{\mathrm{y}}}{4 \pi \varepsilon_0 \mathrm{c}}+\frac{\mathrm{q}_{\mathrm{z}}}{4 \pi \varepsilon_0 \mathrm{c}} \\ & \frac{\sigma 4 \pi \mathrm{a}^2}{\mathrm{a}}-\frac{\sigma 4 \pi \mathrm{b}^2}{\mathrm{~b}}+\frac{\sigma 4 \pi \mathrm{c}^2}{\mathrm{c}}=4 \pi \sigma \frac{\left(\mathrm{a}^2-\mathrm{b}^2+\mathrm{c}^2\right)}{\mathrm{C}} \end{aligned}
\begin{aligned} & c(a-b+c)=a^2-b^2+c^2 \\ & c(a-b)+c^2=(a+b)(a-b) \\ & c(a-b)=(a+b)(a-b) \\ & c=a+b=2+3 \\ & c=5 \mathrm{~cm} \text { Ans. } \end{aligned}

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Irshad Anwar

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