Charge Q is uniformly distributed only on curved surface of a thin hemispherical shell. A,B and C are three points on the circular base of hemisphere, such that A is the centre. Let the electric potential at points A, B and C be `V_A, V_B, V_C` respectively. Then

Options

A. `V_(A) gt V_(B) gt V_(C)`
B. `V_(C) gt V_(B) gt V_(A)`
C. `V_(B) gt V_(A)` and `V_(B) gt V_(C)`
D. `V_(A) =V_(B) = V_(C)`

Answer

D

Explanation

Let the possible direction of electric field at point B be shown by 1,2,3 and 4 (figure 1). Rotate the figure upside down. It will be shown in figure 2

Now on placing upper wall of figure 1 on the lower of figure 2 we get complete sphere. electric field at point B must be zero, which is possible if the electric field is along direction 3. hence electric field at all points on circular base of hemisphere is normal to plane of circular base.
`:.` Circular base of hemisphere is an equipotential surface.
Aliter: consider a shadded circle which divides a uniformly charged thin spherical shell into two equal halves. the potential at points A,B and C lying on the shaded circle is same. the potential at all these points due to upper hemisphere is half that due to complete sphere. hence potential at points A, B and C is also same due to upper hemisphere.