A point charge q is placed at some distance d away from the centre of a grounded conducting sphere of radius r , as shown in the figure. The charge that flows from the earth to the sphere is

Question

A point charge q is placed at some distance d away from the centre of a grounded conducting sphere of radius r , as shown in the figure. The charge that flows from the earth to the sphere is <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-zyca8ftdryfs.png" /> (A) -(qr/d-r) (B) -(qd/d-r) (C) -(qr/d) (D) -(qd/r)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-zyca8ftd7zfm.png" /> Let us assume that the charge flowing from earth to the sphere is q1 . Since the sphere is grounded, its potential will be zero. Hence, (q1/4 π ϵ 0 r)+(q/4π ϵ 0d)=0 q1=-(qr/d)

Q. A point charge $q$ is placed at some distance $d$ away from the centre of a grounded conducting sphere of radius $r$ , as shown in the figure. The charge that flows from the earth to the sphere is

$- \frac{q r}{d - r}$

$- \frac{q d}{d - r}$

$- \frac{q r}{d}$

$- \frac{q d}{r}$

Let us assume that the charge flowing from earth to the sphere is $q_{1}$ . Since the sphere is grounded, its potential will be zero. Hence,
$\frac{q _{1}}{4 π ϵ _{0} r} + \frac{q}{4 π ϵ _{0} d} = 0$
$q_{1} = - \frac{q r}{d}$

Q. A point charge q is placed at some distance d away from the centre of a grounded conducting sphere of radius r , as shown in the figure. The charge that flows from the earth to the sphere is

−d−rqr​

−d−rqd​

−dqr​

−rqd​