37 \times 10^{-6} \, \text{C/m}^2 \times 4\pi (0.250 \, \text{m})^2 = +0.002 \, \text{C}$. When a charge of -0.500 $\mu$C is introduced at the center of the cavity, it will induce an equal and opposite charge on the inner surface of the sphere.
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