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

The correct option is (a).

Step-by-step explanation:

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

`E=(k)/(d^2)`

We can write it as follows :

`(E_1)/(E_2)=((d_2)/(d_1))^2`

Put all the values,

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

So, the correct option is (a).