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A thin hollow cylindrical shell (open at both ends) has radius L and length L. It carries a uniform surface charge density sigma. The electrostatic potential at point P located on the axis at one end of the cylinder is given by V_P = (sigma * L)/(k * epsilon₀) * ln(1 + sqrt(2)). Find the integer value of k.
- 1
- 2
- 3
- 4
Correct answer: 2
Solution
Each elemental ring of width dx at axial distance x from P contributes dV = sigma*L*dx/(2*epsilon₀*sqrt(x²+L²)). Integrating from 0 to L and applying the log integral formula gives V_P = sigma*L*ln(1+sqrt(2))/(2*epsilon₀), so k=2.
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