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  • A charge of 6 µC is given to a hollow metallic sphere of radius 0.2 m. Find the potential at (1) the surface and (ii) the centre of the sphere.

A charge of 6 µC is given to a hollow metallic sphere of radius 0.2 m. Find the potential at (1) the surface and (ii) the centre of the sphere.

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Given charge: $Q = 6\,\mu\text{C} = 6\times10^{-6}\,\text{C}$  
Radius: $R = 0.2\,\text{m}$  
Potential on the surface of a sphere:  
$V = \dfrac{1}{4\pi\varepsilon_0}\dfrac{Q}{R}$  
Using $\dfrac{1}{4\pi\varepsilon_0} = 9\times10^9$,

$V = 9\times10^9 \cdot \dfrac{6\times10^{-6}}{0.2}$

$V = 9\times10^9 \cdot 30\times10^{-6}$

$V = 270\times10^{3}$

$\boxed{V_{\text{surface}} = 2.7\times10^5\ \text{V}}$

For a hollow metallic sphere:  
$V_{\text{centre}} = V_{\text{surface}}$

$\boxed{V_{\text{centre}} = 2.7\times10^5\ \text{V}}$
 

Posted by

Saumya Singh

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