A thin rod of length (2 ell) has a linear charge density that is (lambda_{0}) at the
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A thin rod of length \(2 \ell\) has a linear charge density that is \(\lambda_{0}\) at the left end but decreases linearly with distance going from left to right in such a way that the charge on the entire rod is zero.
(a) What is the magnitude of the electric field along the rod's axis at a position \(\mathrm{P}\) that is a distance \(d>\ell\) to the right of the center of the rod?
(b) Does your expression simplify to a familiar result for the limiting case \(d \gg \ell\) ? (Hint: The dipole moment of the rod has magnitude \(p=2 \lambda_{0} \ell^{2} / 3\).)
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a To find the magnitude of the electric field along the rods axis at position P a distance d ell to the right of the center of the rod we can divide the rod into infinitesimally small charge elements ...View the full answer
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