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Work done in moving a positive charge fr...

Work done in moving a positive charge from the centre of a hollow uniformly charged sphere to its surface is zero. Does it imply that the potential is zero inside the sphere?

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No, potential is not zero but it is constant from the centre to the surface of a hollow uniformly charged sphere. This is because electric field inside a hollow uniformly charged sphere is zero. So, it is an equipotential volume and hence electric potential is the same inside and on the surface of the sphere.
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Knowledge Check

  • The work done in moving a positive charge on an equipotential surface is

    A
    finite and positive
    B
    infinite
    C
    finite and negative
    D
    zero

  • A hollow sphere of copper is positively charged. Then the electric field inside the sphere is

    A
    the same as the field at the surface
    B
    greater than the field at the surface
    C
    ess than the field at the surface but not zero
    D
    zero

  • A hollow metal sphere of radius 5 cm is charged so that the potential on its surface is 10 V . The potential at the centre of the sphere is

    A
    `0 V`
    B
    `10 V`
    C
    same as at point `5 cm` away from the surface
    D
    same as at point `25 cm` away from the surface

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    A hollow metal sphere of radius 5 cm is charged such that the potential on its surface is 10 V. What is the potential at the centre of the sphere?

    A hollow metal sphere of radius 10 cm is charged such that the potential on its surface is 5 V. What is the potential at the centre of the sphere?

    A hollow metal sphere of radius 6 cm is charged such that the potential on its surface is 12 V.What is the potential at the centre of the sphere?

    Statement-1 : No work is done in taking a small positive charge from one point to other inside a positively charged metallic sphere while outside the sphere work is done in taking the charge towards the sphere. Neglect induction due to small charge. Statement-2 : Inside the sphere electric potential is same at each point, but outside it is different for different points.

    There is a ball of radius r having uniformly distributed volume charge Q on it and there is a spherical shell of radius r having uniformly distributed surface charge Q on it. The two spheres are far apart. (a) A point charge q is moved slowly from the centre of the shell (through a small hole in it.) to the centre of the ball. Find work done by the external agent in the process. (b) The two spheres are brought closer so that their centers are separated by 4r. Now calculate the amount of work needed in slowly moving a point charge q from the centre of the shell to the centre of the ball. Assume that charge on one ball does not alter the charge distribution of the other. Does your answers in (a) and (b) differ? Why?

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