Applications of Gauss' Theorem(Field Due to an Infinitely long Charged Wire)

Chapter-1|Electric Charges and Fields | NCERT 12th Physics:

Applications of Gauss' Theorem:

(I) Field Due to an Infinitely long Charged Wire:

We consider a thin infinitely long straight wire having a uniform linear density λ. To determine the field at a distance r from the line charge, we choose a cylindrical Gaussion surface of radius r, length l and with its Axis along the line charge. let it has curved surface S₁ and Flat surface ends S₂ and S₃.

Therefore, Only curved surface contribute the total flux.