Two points are at distance `a` and `b (a lt b)` from a long string of charge per unit length `lambda`. The potential difference between th epoints is proportional to

Options

A. `(b)/(a)`
B. `(b^(2))/(a^(2))`
C. `sqrt((b)/(a))`
D. `ln (b)/(a)`

Answer

4

Explanation

`vec(E ). vec(d r) = E dr`
`V_(2) - V_(1) = - int vec(E ) . Vec( dr) = - (lambda)/(2 pi in_(0)) int_(a)^(b) (dr)/( r)`
` = - (lambda)/(2 pi in_(0)) ln (b//a)`
`(V_(2) - V_(1)) prop ln(b//a)`