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Question

Three concentric metal shells A, B and C of respectively radii a, b and c $$(a < b < c)$$ have surface charge densities $$+\sigma$$, $$-\sigma$$ and $$+\sigma$$ respectively. The potential of shell B is?


A
σϵ0[b2c2b+a]
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B
σϵ0[b2c2c+a]
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C
σϵ0[a2b2a+c]
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D
σϵ0[a2b2b+c]
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Solution

The correct option is D $$\displaystyle\frac{\sigma}{\epsilon_0}\left[\displaystyle\frac{a^2-b^2}{b}+c\right]$$
$$V_{outer} = \dfrac{KQ}{r}$$
where r is distance of point from the centre of shell
$$V_{inside} = \dfrac{KQ}{R}$$
where R is the radius of shell
$$V_B = \dfrac{Kq_A}{r_b} - \dfrac{Kq_B}{r_b} + \dfrac{Kq_C}{r_c}$$
$$V_B =\dfrac{1}{4 \pi \epsilon_o} [\dfrac{\sigma 4 \pi a^2}{b} - \dfrac{\sigma 4 \pi b^2}{b} + \dfrac{\sigma 4 \pi c^2}{c}]$$
$$V_B = \dfrac{\sigma}{\epsilon_o} [ \dfrac{a^2 - b^2}{b} + c]$$

802269_845677_ans_3a1dda98d6bd4fb6bc5b433242698619.JPG

Physics

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