) 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

0.7071D

Explanation:

Electric field strength is given as:

E = kq/r²

Where k = Coulumbs constant

q = charge

r = distance

When r = D, E = 1000 N/C

=> 1000 = kq/D²

=> kq = 1000D² (1)

When E = 2000 N/C,

2000 = kq/r²

kq = 2000r² (2)

Since k is a constant and q is the same, equate (1) & (2):

2000r² = 1000D²

=> r² = 1000/2000 D²

r² = 0.5D²

=> r = 0.7071D