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A sphere encloses an electric dipole with charge $\pm 3 \times 10^{-6} \mathrm{C}$. What is the total electric flux across the sphere?
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zero
When a sphere encloses a charged dipole,
Here, $q= \pm 3 \times 10^{-6} \mathrm{C}$
Thus, according to Gauss's law, the net electric flux across the closed surface is equal to the net charge enclosed by it divided by $\varepsilon_0$, i.e.
$\phi_{\mathrm{E}}=\frac{\mathrm{q}_{\mathrm{in}}}{\varepsilon_0}=\frac{+3 \times 10^{-6}-3 \times 10^{-6}}{\varepsilon_0}=0$
Hence, electric flux across the sphere is zero.
Here, $q= \pm 3 \times 10^{-6} \mathrm{C}$
Thus, according to Gauss's law, the net electric flux across the closed surface is equal to the net charge enclosed by it divided by $\varepsilon_0$, i.e.
$\phi_{\mathrm{E}}=\frac{\mathrm{q}_{\mathrm{in}}}{\varepsilon_0}=\frac{+3 \times 10^{-6}-3 \times 10^{-6}}{\varepsilon_0}=0$
Hence, electric flux across the sphere is zero.
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