A conical surface (an empty ice-cream cone) with surface charge density ? has height h.Radius of the top is R.Find potential difference between vertex & center of the top.FSP0251032301.jpgFSZ

permaneceerc

permaneceerc

Answered question

2021-02-14

A conical surface (an empty ice-cream cone) with surface charge density ? has height h.Radius of the top is R.Find potential difference between vertex & center of the top.
image

Answer & Explanation

saiyansruleA

saiyansruleA

Skilled2021-02-15Added 110 answers

Consider the figure as this one (the answer will be the same)
image
The thin strip (a height z above the axis) is a ring of radius (ϵ and an expression for r in terms of z to find its contribution to V(a), as it is a ring:
Vrg,aξs=12ϵ0(λrz2+r2)
Then we will integrate summing all the rings.
By similar triangles
rz=Rh
,so
r=Rhz
Area of the strip =
2πrdl=2πrdzcosθ=2πrhR2+h2dz
image NKS So θ=σR2+h2hdz
so the potential in a is
V(a)=σR2+h22hϵ0(Rh)0kzdz(Rh)2z2+z2=σR2ϵ0
image
image

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