An electric field is uniform throughout a certain region of space. Its magnitude is \(10~\mbox{V/m}\). A conducting sphere of radius \(R=1~\mbox{cm} \) and charge \(Q=1~\mu\mbox{C}\) is then placed in this region. Determine the magnitude of the electric field at the center of the sphere.

**Details and assumptions**

- \(k=\frac{1}{4\pi \epsilon_{0}}=9\times 10^{9}~\mbox{N m}^{2}/\mbox{C}^{2} \)

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