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A uniformly charged conducting sphere of $2.4 \mathrm{~m}$ diameter has a surface charge density of $80.0 \mu \mathrm{C} \mathrm{m}^{-2}$. The charge on the sphere is nearly
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Verified Answer
The correct answer is:
$1.45 \times 10^{-3} \mathrm{C}$
Diameter of sphere $\mathrm{d}=2.4 \mathrm{~m}$
Radius, $\mathrm{r}=\frac{\mathrm{d}}{2}=1.2 \mathrm{~m}$
Surface charge density, $\sigma=80 \times 10^{-6} \mathrm{C} \mathrm{m}^{-2}$
Charge on the sphere, $\mathrm{Q}=\sigma \mathrm{A}$
$$
\begin{aligned}
& =\sigma\left(4 \pi \mathrm{r}^2\right) \\
& =80 \times 10^{-6} \times 3.14 \times(1.2)^2=1.45 \times 10^{-3} \mathrm{C}
\end{aligned}
$$
Radius, $\mathrm{r}=\frac{\mathrm{d}}{2}=1.2 \mathrm{~m}$
Surface charge density, $\sigma=80 \times 10^{-6} \mathrm{C} \mathrm{m}^{-2}$
Charge on the sphere, $\mathrm{Q}=\sigma \mathrm{A}$
$$
\begin{aligned}
& =\sigma\left(4 \pi \mathrm{r}^2\right) \\
& =80 \times 10^{-6} \times 3.14 \times(1.2)^2=1.45 \times 10^{-3} \mathrm{C}
\end{aligned}
$$
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