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(a) State Gauss's law. Using this law, o...

(a) State Gauss's law. Using this law, obtain the expression for the electric field due to an infinitely long straight conductor of linear charge desntiy `lamda`.
(b) A wire AB of length L has linear charge density `lamda = 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 the electric flux through this surface.

Text Solution

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(a) Gauss's Law
(b) length = L
`lamda = kx`
`:. lamda = (Q)/(L)`
charge on elementary length 'dx' at a distance x from end A is
`kx = (Q)/(L) " " dq = lamda dx`
`rArr Q = kxL " " dq = kxdx`
Now, `q = (kx L)/(epsi_(0)) " " :.` total charge on the road = `int dr = underset(0)overset(L)int kxdx`
`Q = (kxL)/(epsi_(0)) " " q = (kL^(2))/(2)`
`:.` flux emitted by the charged rod and passing through the Gaussian surface.
`psi = (q)/(in_(0)) " " |psi = (KL^(2))/(2 in_(0))|`
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