Question

# A hollow metal sphere of radius $20cm$ is charged such that the potential on its surface is $120Volt.$ The potential at the centre of the sphere is

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Solution

## Step 1. Given dataPotential on the surface $V$$=120Volt.$Radius of the sphere $r=20cm$Step 2. Formula used Potential $V$$=\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.Thus it can conduct electricity.We know that there is no electric field inside the hollow sphere.Electric potential is defined as the work done per unit coulomb against the electric field to move the charge from a reference point to a measuring pointGiven electric potential is $120Volt.$Since the electric field is zero inside the sphere, the potential will be the same everywhere inside the sphere and equal to the potential at the surface.Thus the potential at the center is $120Volt.$Hence, the potential at the center of the sphere is $120Volt.$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 $r the electric field will be zero for the metallic charged sphere.$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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