Determine The Induced Charge

Consider a dielectric thin rod with total charge \(q=1~\mu\text{C}\) uniformly distributed over its length. The rod touches a grounded conducting sphere of radius \(R=50~\text{cm}\) as shown in the figure below. Find the charged induced in the sphere in microcoulombs if the length of the rod is \(L=1~\text{m}\). The following integral may be useful: \[\int \frac{1}{\sqrt{a^{2}+x^{2}}}dx=\ln(x+\sqrt{x^2+a^{2}})+C.\]

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