A point charge of magnitude $+1 \mu \mathrm{C}$ is fixed at $(0$, $0,0)$. An isolated uncharged spherical…

A point charge of magnitude $+1 \mu \mathrm{C}$ is fixed at $(0$, $0,0)$. An isolated uncharged spherical conductor, is fixed with its center at $(4,0,0)$. The potential and the induced electric field at the centre of the sphere is :
  1. $1.8 \times 10^5 \mathrm{~V}$ and $-5.625 \times 10^6 \mathrm{~V} / \mathrm{m}$
  2. $0 \mathrm{~V}$ and $0 \mathrm{~V} / \mathrm{m}$
  3. $2.25 \times 10^5 \mathrm{~V}$ and $-5.625 \times 10^6 \mathrm{~V} / \mathrm{m}$
  4. $2.25 \times 10^5 \mathrm{~V}$ and $0 \mathrm{~V} / \mathrm{m}$

Solution

$\mathrm{q}=1 \mu \mathrm{C}=1 \times 10^{-6} \mathrm{C}$ $ \mathrm{r}=4 \mathrm{~cm}=4 \times 10^{-2} \mathrm{~m} $ Potential $\mathrm{V}=\frac{\mathrm{kq}}{\mathrm{r}}$ $ \begin{aligned} & =\frac{9 \times 10^9 \times 10^{-6}}{4 \times 10^{-2}} \\ & =2.25 \times 10^5 \mathrm{~V} . \end{aligned} $ Induced electric field $\mathrm{E}=-\frac{\mathrm{kq}}{\mathrm{r}^2}$ $ =\frac{9 \times 10^9 \times 1 \times 10^{-6}}{16 \times 10^{-4}}=-5.625 \times 10^6 \mathrm{~V} / \mathrm{m} $

Asked in: JEE Main 2013 (22 Apr Online)

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