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nilesthebrave
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Homework Statement
A line charge in the x directio has a variable charge density given by the equation λ=4 λnot((1-x)/2L), where λnot is a constant. The rod has a length of L.
i)What is the net charge of the rod? Hint-the net charge is calculated by integrating the charge density with respect to x.
ii)Show that the electric field at the origin is given as E=-((2kQ)/L^2) (1-ln2)i
Homework Equations
Q=∫λrdx
Ex=(kλdx)/r^2
The Attempt at a Solution
Well I couldn't find much about something like this, so I kind of winged it and have no idea if what I did was even partially right but here we go.
i)Q=∫λrdx
=4λnot∫(1-(x/2L))/L^2 dx
=4λ (x-4L)/4L^2
Q=(λx-4L)/L^2
Again I'm not sure I'm doing that right, but it's what made sense to me.
ii)dEx=((kλdx)/r^2) (x/r)
Ex=kλx∫dx/r^3
Ex=kλx[-1/2r^2]
And now I have no idea what I'm doing...
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