Answer:
Distance from the line with the field strength of 2000N/C = 0.7071 D or D√(0.5) or D/(√2)
Explanation:
Electric field is given by,
E = kQ/r²
where k = constant, Q = total charges, R = distance from the line of charge = D
Provided, total charges are constant, then,
The electric field is inversely proportional to the square of D.
E ∝1/D²
E = c/D²
c represents kQ, the two constant parameters.
1000 = c/D²
c = 1000D²
For E = 2000 N/C
Let the distance from the line with that field strength be x
E = kQ/x²
E ∝1/x²
E = c/x²
2000 = c/x²
c = 1000D²
2000 = 1000D²/x²
x² = 0.5D²
x = √(0.5D²)
x = D√0.5
x = 0.7071 D or D√(0.5) or D/(√2)
Hope this Helps!!!