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

Answer 1

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!!!