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 the figure. Their interface lies in x -y plane. Which of the following statement(s) is/are correct?

The field at all points of x-y plane within the sphere points in the ve z-direction

All points of the x -y plane within the sphere are equipotential

The field at all points on z-axis outside the sphere point along positive z-direction

The field at points on z-axis which are on either side of origin outside the sphere is in opposite directions

JEE Advanced 2020 Full Test 5 Paper 1

Question : 4 of 54

Marks: +1, -0

A hollow, insulating spherical shell has a surface charge distribution placed upon it, such that the upper hemisphere has a uniform surface charge density +σ, while the lower hemisphere has a uniform surface charge density −σ, as shown in the figure. Their interface lies in x -y plane. Which of the following statement(s) is/are correct?

The field at all points of x−y plane within the sphere points in the ve z-direction
All points of the x -y plane within the sphere are equipotential
The field at all points on z-axis outside the sphere point along positive z-direction
The field at points on z-axis which are on either side of origin outside the sphere is in opposite directions

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