Which of the following statement is false for a perfect conductor in electrostatic condition?

Options:

The surface of the conductor is an equipotential surface.

The electric field lines just outside the surface of a conductor is perpendicular to the surface.

The electric field is continuous across the surface of conductor.

The electric field is discontinuous across the surface of conductor.

Dear Student,
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The false statement in the given set of statements is: The electric field is continuous across the surface of the conductor.
Please go through the explanation for each case below:

1. The surface of the conductor is an equipotential surface: True
We that Electric field is perpendicular to the surface of the conductor thus, there is no component of the electric field along a conducting surface under electrostatic conditions, so no work is done in moving the charge around the surface, thus no difference in potential.

2. Electric Field lines just outside the surface of conductor are perpendicular to the surface - True
    It is a consequence of explanation provided in 1 if the field has any direction other than perpendicular then work done to move charge on the surface is not zero, and thus it will no longer be equipotential, which is not true.

3. Electric Field across the surface of the conductor is continuous - False
We know, since entire charge resides on the surface of the conductor due to Coulomb's Law. As a consequence, we know that the electric field inside a spherical shell is zero, while outside it is not zero. Thus the across the surface electric field is discontinuous.

4. Electric Field across the surface of the conductor is discontinuous - True
Reason explained in 3.

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