A uniformly charged conducting sphere of $2.4 \mathrm{~m}$ diameter has a surface charge density of $80.0…

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
  1. $2.5 \times 10^{-3} \mathrm{C}$
  2. $1.45 \times 10^{-3} \mathrm{C}$
  3. $6.5 \times 10^{-3} \mathrm{C}$
  4. $0.15 \times 10^{-3} \mathrm{C}$

Solution

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} $

Asked in: AP EAMCET 2023 (19 May Shift 1)

Practice more Electrostatics questions on Aicharya