Lines of charge: At a distance D from a very long (essentially infinite) uniform line of charge, the electric field strength is 1000 N/C. At what distance from the line will the field strength to be 2000 N/C?
A) 2D
B) D
C) D/
D) D/2
E) D/4

Question

Lines of charge: At a distance D from a very long (essentially infinite) uniform line of charge, the electric field strength is 1000 N/C. At what distance from the line will the field strength to be 2000 N/C?
A) 2D 
B) D 
C) D/ 
D) D/2 
E) D/4

Quizplus · Accepted Answer

The electric field strength of a uniformly charged infinitely long line is given by $E=\frac{\lambda}{2\pi\epsilon_0 r}$, where $\lambda$ is the charge density of the line and $r$ is the distance from the line. We can use this formula to set up a ratio of electric field strengths: 
\begin{align*}
\frac{E_1}{E_2} &= \frac{\frac{\lambda}{2\pi\epsilon_0 D}}{\frac{\lambda}{2\pi\epsilon_0 r}} \
\frac{1000	ext{ N/C}}{2000	ext{ N/C}} &= \frac{D}{r} \
\frac{1}{2} &= \frac{D}{r} \
r &= 2D
\end{align*}
Therefore, the answer is (A).

Lines of Charge: at a Distance D from a Very