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A rod of length 'l' is placed along x-a...

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 `lambda=` a, a being a positive constant. Electric potential at P as shown in the figure is -

A

`(a)/(4pi epsilon_(0)) ln((b+l)/(b))`

B

`(a)/(4pi epsilon_(0)) "ln" (l)/(b)`

C

`(a)/(4pi epsilon_(0)) "ln"(b)/(l)`

D

zero

Text Solution

Verified by Experts

The correct Answer is:
A

`V= int_(b)^(b+l) (kdq)/(x) = int_(b)^(b+l) (k lambda dx)/(x) =ka int_(b)^(b+l) (dx)/(x)`
`V="Ka ln"((b+l)/(b))`
`V=(a)/(4pi epsilon_(0)) "ln"((b+l)/(b))`
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