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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 data

The potential on the surface V=10Volt.

The radius of the sphere r=5cm

Step 2. Formula used

Potential is given as,

V=14πε0·qr

Where q is the charge and ε0 is the permeability and r is the radius

Step 3. Find the potential at the center of the sphere

The 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=14πε0·Qr2,r>Rif r<R the electric field will be zero for metallic charged sphere.

V=14πε0·Qr,r>Rif r<R the potential will be constant throughout the metallic charged sphere.


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