Determine The Induced Charge

Consider a dielectric thin rod with total charge q=1 μCq=1~\mu\text{C} uniformly distributed over its length. The rod touches a grounded conducting sphere of radius R=50 cmR=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 mL=1~\text{m}. The following integral may be useful: 1a2+x2dx=ln(x+x2+a2)+C.\int \frac{1}{\sqrt{a^{2}+x^{2}}}dx=\ln(x+\sqrt{x^2+a^{2}})+C.

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