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A rod of length l is placed along x -axis. One of its ends is at the origin. The rod has a non-uniform charge density λ = a x , a being a positive constant. Electric potential at P as shown in the figure is

Options

  1. Aa 4 π ε 0 ln b + l b
  2. Ba 4 π ε 0 ln l b
  3. Ca 4 π ε 0 ln b l
  4. Dzero

Correct answer

A. a 4 π ε 0 ln b + l b

Step-by-step solution

V   = ∫ b b + l k d q x = ∫ b b + l k λ d x x =   k a   ∫ b b + l d x x V = K a   ln b + l b   V   = a 4 π ε 0 ln b + l b  

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