Question Number 104572 by ajfour last updated on 22/Jul/20

Commented byajfour last updated on 22/Jul/20

A point charge q with mass m  is released at a distance a from  a fixed uniformly charged rod  of length L, charge Q. Find the  speed acquired by point charge  q as it reaches an infinite  distance from the rod.

Answered by OlafThorendsen last updated on 22/Jul/20

E = (Q/(2πε_0 )).(1/x).(1/(x+L))  F = qE = mx^(••)   ((qQ)/(2πε_0 )).(1/(x(x+L))) = mx^(••)   ((qQ)/(2πε_0 L)).(x^• /(x(x+L))) = mx^(••) x^•  (with v = x^• )  ((qQ)/(2πε_0 L^2 ))x^• [(1/x)−(1/(x+L))] = mx^(••) x^•   ((qQ)/(2πε_0 L^2 )).ln(x/(x+L)) = (1/2)mv^2 +C  t = 0, v = 0 ⇒ C = −((qQ)/(2πε_0 L^2 )).ln(a/(a+L))  (1/2)mv^2  = ((qQ)/(2πε_0 L^2 ))(ln(x/(x+L))−ln(a/(a+L)))  v_∞ ^2  = ((qQ)/(πε_0 mL^2 ))ln((a+L)/a)  ...may be

Commented byajfour last updated on 22/Jul/20

Dont you think Sir,  E=(Q/(4πε_0 ))(1/(x(x+L)))    ?