A solid, uncharged conducting sphere of radius 3a contains a concentric hollowed spherical cavity of radius a . A point charge +Q is placed at the center of the spheres. Taking V=0 at r arrow ∈ fty , the potential at position r=2a from the center is-

Question

A solid, uncharged conducting sphere of radius 3a contains a concentric hollowed spherical cavity of radius a . <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-qoibbihxwz6wvo34.jpg" /> A point charge +Q is placed at the center of the spheres. Taking V=0 at r arrow ∈ fty , the potential at position r=2a from the center is- (A) (K Q/a) (B) (K Q/2 a) (C) (K Q/3 a) (D) (2 K Q/3 a)

Tardigrade Admin · Accepted Answer

Final Charge distribution will be as shown <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-qoibbihxwz6wmpvd.jpg" /> Therefore potential at r=2a is given by V=(K Q/2 a)-(K Q/2 a)+(K Q/3 a) V=(K Q/3 a)

Q. A solid, uncharged conducting sphere of radius $3 a$ contains a concentric hollowed spherical cavity of radius $a$ .

A point charge $+ Q$ is placed at the center of the spheres. Taking $V = 0$ at $r \to\in f t y$ , the potential at position $r = 2 a$ from the center is-

$\frac{K Q}{a}$

$\frac{K Q}{2 a}$

$\frac{K Q}{3 a}$

$\frac{2 K Q}{3 a}$

Final Charge distribution will be as shown

Therefore potential at $r = 2 a$ is given by
$V = \frac{K Q}{2 a} - \frac{K Q}{2 a} + \frac{K Q}{3 a}$
$V = \frac{K Q}{3 a}$

Q. A solid, uncharged conducting sphere of radius 3a contains a concentric hollowed spherical cavity of radius a . A point charge +Q is placed at the center of the spheres. Taking V=0 at r→∈fty , the potential at position r=2a from the center is-

aKQ​

2aKQ​

3aKQ​

3a2KQ​