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Question

Quarter non-conducting disc of radius 4R having uniform surface charge density σ is placed in xz-plane, then which of the following is correct?

A
Electric potential at (0,3R,0)isσ R4ϵ0
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B
Electric potential at (0,0,0) is σ R2ϵ0
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C
Electric field at (0,3R,0) is symmetric with x and z axis
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D
Electric field intensity at (-4R, 0, -4R) is equally inclined with x and z axis
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Solution

The correct options are
A Electric potential at (0,3R,0)isσ R4ϵ0
B Electric potential at (0,0,0) is σ R2ϵ0
C Electric field at (0,3R,0) is symmetric with x and z axis
D Electric field intensity at (-4R, 0, -4R) is equally inclined with x and z axis
(A)V=4R0Kπ2rdrσr2+(3R)2=σ R4ϵ0
(B)V=4R0Kπ2rdr σr=σ R2ϵ0
(C) Given point is symmetric w.r.t x-axis and z-axis.
(D) Given point is symmetric w.r.t x-axis and z-axis.

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