Question

(1) Electric field due to an infinitely long
charged
wire
Consider an infinitely long straight wire
- $B-d
S E dut​

Answer 1

Answer:

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Gauss's law :

The law relates the flux through any closed surface and the net charge enclosed with in the surface. The law states that the total flux of the electric field E over any closed surface.....

This closed imaginary surface is called Gaussian surface. Gauss's law tells us that the flux of E through a closed surface S depends only on the value of net charge inside the surface and not on the location of the charges. Charges outside the surface will not contribute to flux.

Electric field due to an infinitely long straight uniformly charged wire :

Consider an uniformly charged wire of infinite length having a constant linear charge density λ (Charge per unit length). Let P be a point at a distance r from the wire and E be the electric field at the point P. A cylinder of length l, radius r, closed at each end by plane caps normal to the axis is chosen as Gaussian surface. Consider a very small area ds on the Gaussian surface. By symmetry, the magnitude of the electric field will be the same at all points on the curved surface of the cylinder and directed radially outward. .....

Answer 2

Consider a uniformly charged infinitely long thin wire of surface charge density lambda. We wish to find its electric field at a distance of r from it. ... Now at the top and bottom phases of cylinder i.e. its base and top E and dS are perpendicular to each other hence it does not contributes to electric flux.