Three identical metallic uncharged spheres A, B, and C, each of radius a, are kept at the corners of an equilateral triangle of side d(da) as shown in figure. The fourth sphere (of radius a ), which has a charge q, touches A and is then removed to a position far away. B is earthed and then the earth connection is removed. C is then earthed. The charge on C is

Question

Three identical metallic uncharged spheres A, B, and C, each of radius a, are kept at the corners of an equilateral triangle of side d(d>>a) as shown in figure. The fourth sphere (of radius a ), which has a charge q, touches A and is then removed to a position far away. B is earthed and then the earth connection is removed. C is then earthed. The charge on C is (A) (q a/2 d)((2 d-a/2 d)) (B) (q a/2 d)((2 d-a/d)) (C) -(q a/2 d)((d-a/d)) (D) (2 q a/d)((d-a/2 d))

Tardigrade Admin · Accepted Answer

(k q1/a)+(k q/2 d)=0 or q1=(-q a/2 d) (k q2/a)+(k q/2 d)+(k q1/d)=0 or q2=(-q a/2 d)((d-a/d)) <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/a1e815dfcb68f82006c6218aa521509f-.png" />

$\frac{q a}{2 d} (\frac{2 d - a}{2 d})$

$\frac{q a}{2 d} (\frac{2 d - a}{d})$

$- \frac{q a}{2 d} (\frac{d - a}{d})$

$\frac{2 q a}{d} (\frac{d - a}{2 d})$

$\frac{k q _{1}}{a} + \frac{k q}{2 d} = 0$ or $q_{1} = \frac{- q a}{2 d}$
$\frac{k q _{2}}{a} + \frac{k q}{2 d} + \frac{k q _{1}}{d} = 0$
or $q_{2} = \frac{- q a}{2 d} (\frac{d - a}{d})$

2dqa​(2d2d−a​)

2dqa​(d2d−a​)

−2dqa​(dd−a​)

d2qa​(2dd−a​)

akq1​​+2dkq​=0 or q1​=2d−qa​ akq2​​+2dkq​+dkq1​​=0 or q2​=2d−qa​(dd−a​)

$\frac{q a}{2 d} (\frac{2 d - a}{2 d})$

$\frac{q a}{2 d} (\frac{2 d - a}{d})$

$- \frac{q a}{2 d} (\frac{d - a}{d})$

$\frac{2 q a}{d} (\frac{d - a}{2 d})$

$\frac{k q _{1}}{a} + \frac{k q}{2 d} = 0$ or $q_{1} = \frac{- q a}{2 d}$
$\frac{k q _{2}}{a} + \frac{k q}{2 d} + \frac{k q _{1}}{d} = 0$
or $q_{2} = \frac{- q a}{2 d} (\frac{d - a}{d})$