1.

A wire AB of length L has linear charge density `lambda = Kx`, where x is measured from the end A of the wire. This wire is enclosed by a Gaussian hollow surface. Find the expression for electric flux through the surface`.

Answer» Here, `lambda = (dq)/(dx) = kx` ,
`sigma = ?`
dq = Kx dx
Total charge on the wire
`q = int_(0)^(L) kx dx = [(Kx^(2))/(2)]_(0)^(L) = (KL^(2))/(2)`
Electric flux through the Gaussion hollow surface is
`sigma = (q)/(in_(0)) = (KL^(2))/(2in_(0))`


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