A uniformly charged conducting sphere of diameter 14 cm has surface charge density of $40 \mu…

A uniformly charged conducting sphere of diameter 14 cm has surface charge density of $40 \mu \mathrm{Cm}^{-2}$. The total electric flux leaving the surface of the sphere is nearly (Permittivity of free space $=8.85 \times 10^{-12}$ SI unit )
  1. 40 kWb
  2. 140 kWb
  3. 240 kWb
  4. 280 kWb

Solution

Electric flux $\phi=\frac{\mathrm{q}}{\varepsilon_0}=\frac{4 \pi \mathrm{r}^2 \sigma}{\varepsilon_0}$ $\begin{aligned} & =\frac{4 \times 3.14 \times\left(7 \times 10^{-2}\right)^2 \times 40 \times 10^{-6}}{8.85 \times 10^{-12}} \\ & =\frac{4 \times 3.14 \times 49 \times 10^{-4} \times 4 \times 10^{-5}}{8.85 \times 10^{-12}} \\ & =\frac{4 \times 3.14 \times 49 \times 4 \times 10^3}{8.85} \\ & =278 \times 10^3 \approx 280 \times 10^3 \mathrm{~Wb} \\ & =280 \mathrm{kWb}\end{aligned}$

Asked in: MHT CET 2024 (02 May Shift 1)

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