A very long straight wire has charge per unit length 1.56×10−10 C/m .

At what distance from the wire is the magnitude of the electric field equal to 2.40 N/C ?
Use 8.85×10−12 C2/(N⋅m2) for the permittivity of free space, and use π=3.14159.

Given:

By using the Gauss law, we get

→

or,

→  

Thus the above approach is right.  

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The magnitude of the electric field equal to 2.40 N/C at 1.1537m from the wire.

Explanation:

using Guass law,

(guessing that a cylinder of radius r and length L around wire such that wire is at centre )

E. A = qin / e0

E ( 2πr L ) = (1.56 x x L) / (8.85 x )

E = (1.56 x ) / (2πr x 8.85 x  )

so 2.40 = (1.54 x ) / (2πr x 8.85 x )

2.40 (6.284r) = 0.174 x 10²

15.0816r = 17.4

r = 1.1537m