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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. The electric potential at the point P (origin) as shown in the figure is

Options

  1. AV = a 4 π ε 0 l b b + l  
  2. BV = a 4 π ε 0 b l b + l  
  3. CV = a 4 π ε 0 b l  
  4. DV = a 4 π ε 0 l b  

Correct answer

A. V = a 4 π ε 0 l b b + l  

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 2 V = k a   1 b - 1 b + l V = a 4 π ε 0 l b b + l  

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