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# A charged rod of length $L$ produces an electric field at point $P(a, b)$ given by$$E(P) = \int_{-a}^{L - a} \frac{\lambda b}{4 \pi \varepsilon_0 (x^2 + b^2)^{\frac{3}{2}}}\ dx$$where $\lambda$ is the charge density per unit length on the rod and $\varepsilon_0$ is the free space permittivity (see the figure). Evaluate the integral to determine an expression for the electric field $E(P)$.

## the expression for electric field $\mathrm{E}(\mathrm{P})=\frac{k}{4 \pi c b}\left(\frac{L-a}{\sqrt{(L-a)^{2}+b^{2}}}+\frac{a}{\sqrt{a^{2}+b^{2}}}\right)$

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Integration Techniques

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