Consider a hollow, infinite sphere of radius R. the hollow space is free of charge, but...

Consider a hollow, infinite sphere of radius R. the hollow space is free of charge, but a surface charge sigma = sigma not cos theta exists on the inside surface of the conductor at s =R. Can this sphere be a conductor? ( I.e, can you induce this charge on a conducting surface somehow)

Expert Solution

Answer : The sphere is a conductor for any conducting surface placed outside the sphere. But is not a conductor if the conducting surface is inside the sphere.

This is due to Gauss law which states that the electric flux coming out of a closed surface is 1/ times the charge enclosed inside the closed surface. So inside the sphere the charged enclosed would be zero as the charge is on the inner surface of the sphere. And the Electric field = Electric flux/ enclosed Area, so the field is also zero. Outside the sphere the charged enclosed would be the entire charge on the sphere hence it would exert an electric field and thus induce charge. Where the charge exists on the sphere is immeterial.

P.S: I think the answer would be that it cannot be a conductor as the sphere is said to be infinite. Maybe theyare suggesting that no surface can hence exist outside this sphere. But I wanted to clarify the logic.

genius_generous answered 2 years ago

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