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State Gauss' law.Using this law obtain t...

State Gauss' law.Using this law obtain the expression for the electric field due to an infinitely long straight conductor of linear charge density `lambda `
(ii) A wire AB of length L has linear charge `lambda =kx,` where x is measured from the end A of the wire. The wire is enclosed by a Gaussian hollow surface.Find the expression for the electric flux through the surface.

Text Solution

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Let as as shown be an element of wire AB situated at a distance x from end A of wire and of thickness dx.
Then charge on this element `dg=lambda dx=kx dx `
` therefore `Total charge on wire `AB ,q = int dq =underset o oversetto L int kx dx =(1)/(2) kL^(2) `
` therefore ` In accordance with Gauss.law ,total electric flux through the enclosed Gaussian surface `phi_in `
` = (q)/(in_0) =(kL^(2)) /( 2 in _0) `
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