Electrostatics problem involving Cone

1. The problem statement, all variables and given/known data

A cone made of insulating material has a total charge Q spread uniformly over its sloping surface. Calculate the energy required to take a test charge q from infinity to apex A of cone. The slant length is L.

2. Relevant equations

3. The attempt at a solution

Potential at the tip of the cone is calculated by adding potentials due to rings of charges .

Let us consider a ring having charge ‘dq’ at a distance ‘x’ from the tip and at slant height L’. L’=xsecθ where θ is the half angle of the cone .

The surface area dS of the ring = 2π√(L’2-x2)dx

dq=Q(dS)/(πRL)

V = ∫dV = ∫kdq/L’

This doesn’t give me correct answer .I am not sure if I have approached the problem correctly.

I would be grateful if somebody could help me with the problem.

Attached Images
File Type: jpg cone.JPG (4.9 KB)

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