Question

# A hollow metal sphere of radius $5cm$ is charged such that the potential on its surface is $10Volt.$ The potential at the center of the sphere is

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Solution

## Step 1. Given dataThe potential on the surface $V$$=10Volt.$The radius of the sphere $r=5cm$Step 2. Formula used Potential is given as, $V$$=\frac{1}{4\pi {\epsilon }_{0}}·\frac{q}{r}$Where $q$ is the charge and ${\mathrm{\epsilon }}_{0}$ is the permeability and $r$ is the radius Step 3. Find the potential at the center of the sphereThe sphere is hollow and made of metal and it can conduct electricity. We know that there is no electric field inside the hollow sphere.Since the electric field is zero inside the sphere, the potential will be same everywhere inside the sphere. Given electric potential is $10Volt.$ Thus the potential at the center is $10Volt.$Hence, the potential at the centre of the sphere is $10Volt.$Note:Let $R$ re the radius of the sphere $E$ the electric field and $P$ the potential, $Q$ is the charge $E=\frac{1}{4\pi {\epsilon }_{0}}·\frac{Q}{{r}^{2}},r>R$if $r the electric field will be zero for metallic charged sphere.$V=\frac{1}{4\pi {\epsilon }_{0}}·\frac{Q}{r},r>R$if $r the potential will be constant throughout the metallic charged sphere.

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