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))) ?