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Question

A hollow metal sphere of radius 10cm is charged such that the potential on its surface is 80volt. The potential at the center of the sphere is


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Solution

Step 1. Given data

Potential on the surface V=80volt.

The radius of the sphere r=10cm

Step 2. Formula used

Potential V=14πε0·qr

Where q is the charge and ε0 is the permittivity and r is the radius,

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

  1. The sphere is hollow and made of metal.
  2. Thus it can conduct electricity.
  3. We know that there is no electric field inside the hollow sphere.
  4. 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 point
  5. Given electric potential is 80volt.
  6. Since the electric field is zero inside the sphere, the potential will be the same everywhere inside the sphere.
  7. Thus the potential at the center is 80volt.

Hence, the potential at the center of the sphere is 80volt.

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 the metallic charged sphere

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


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