Three concentric conducting spherical shells have radii r , 2 r and 3 r respectively. In the state shown charges are q 1 , q 2 and q 3 are present on innermost, middle and outermost shells respe

Question

Three concentric conducting spherical shells have radii r , 2 r and 3 r respectively. In the state shown charges are q 1 ​ , q 2 ​ and q 3 ​ are present on innermost, middle and outermost shells respectively. Then select correct alternative(s).

TestHub · Accepted Answer

In the state shown, the innermost and outermost shells are grounded.

$V (3 r) = 0$ : $q_{1} + q_{2} + q_{3} = 0$ - (A)

$V (r) = 0$ : $q_{1} + \frac{q _{2}}{2} + \frac{q _{3}}{3} = 0$ ; subtracting twice the first equation: $4 q_{1} + q_{2} = 0$ ⇒ $q_{1} = - \frac{q _{2}}{4}$ - (B)

Then $q_{3} = - q_{1} - q_{2} = - \frac{3 q _{2}}{4}$ , so $\frac{q _{3}}{q _{1}} = 3$ - (C); $\frac{q _{3}}{q _{2}} = - \frac{3}{4} \neq = - \frac{1}{3}$ - (D) wrong.

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Options:(select one or more)

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