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A hollow insulated conduction sphere is given a positive charge of $10 \mu \mathrm{C}$. What will be the electric field at the centre of the sphere if its radius is 2 metres?
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2074 Upvotes
Verified Answer
The correct answer is:
Zero
Charge resides on the outer surface of a conducting hollow sphere of radius $\mathrm{R}$. We consider a spherical surface of radius $r < R$. By Gauss theorem
$$
\begin{array}{l}
\int_{\mathrm{s}} \overrightarrow{\mathrm{E}} \cdot \mathrm{ds}=\frac{1}{\varepsilon_{0}} \times \operatorname{ch} a r g \mathrm{e} \quad \text { enclosed or } \\
\mathrm{E} \times 4 \pi \mathrm{r}^{2}=\frac{1}{\varepsilon_{0}} \times 0 \Rightarrow \mathrm{E}=0
\end{array}
$$
i.e electric field inside a hollow sphere is zero.
$$
\begin{array}{l}
\int_{\mathrm{s}} \overrightarrow{\mathrm{E}} \cdot \mathrm{ds}=\frac{1}{\varepsilon_{0}} \times \operatorname{ch} a r g \mathrm{e} \quad \text { enclosed or } \\
\mathrm{E} \times 4 \pi \mathrm{r}^{2}=\frac{1}{\varepsilon_{0}} \times 0 \Rightarrow \mathrm{E}=0
\end{array}
$$
i.e electric field inside a hollow sphere is zero.
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