Question

A hollow, insulating spherical shell has a surface charge distribution placed upon it, such that the upper hemisphere has a uniform surface charge density $+\sigma ,$ while the lower hemisphere has a uniform surface charge density $–\sigma ,$ as shown in figure. Their interface lies in x - y plane. Which of the following statement(s) is/are correct?
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• A. Field at all points on z-axis outside the sphere is in positive z-direction
• B. The field at all points on x - y plane within the sphere is in negative z direction.
• C. Field at points on z-axis which are on either side of origin outside the sphere is in opposite direction
• D. For all the points on the x - y plane within the sphere the electric field is not always perpendicular to x-y plane

Answer 1

Answer: (A), (B)

The field at all points on x - y plane within the sphere is in negative z direction.

Since field is perpendicular to x-y plane inside the sphere. So all points must be at same potential. And because of symmetrical distribution field outside the region on z-axis must be along positive z-axis itself.