Question

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. D/√2.
b. √2D.
c. D/2.
d. 2D.
e. D/4.

Answer 1

Answer:

The correct option is (a).

Explanation:

We know that, the E is inversely proportional to the distance as follows :

$E=\dfrac{k}{d^2}$

We can write it as follows :

$\dfrac{E_1}{E_2}=(\dfrac{d_2}{d_1})^2$

Put all the values,

$\dfrac{1000}{2000}=(\dfrac{d_2}{d})^2\\\\\sqrt{\dfrac{1000}{2000}}=(\dfrac{d_2}{D})\\\\0.7071=\dfrac{d_2}{d}\\\\d_1=0.7071D\\\\d_1=\dfrac{D}{\sqrt2}$

So, the correct option is (a).