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  4. 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 />

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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



Question

NTA AbhyasNTA Abhyas 2020Electrostatic Potential and Capacitance

Solution:

Solution
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,
$\frac{q_{1}}{4 \pi \epsilon _{0} r}+\frac{q}{4\pi \epsilon _{0}d}=0$
$q_{1}=-\frac{qr}{d}$