Magnitude of electric force on 2, μ ,C charge placed at centre O of two equilateral tria

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1. Electric Charges and Fields

hard

The magnitude of electric force on $2\, \mu \,C$ charge placed at the centre $O$ of two equilateral triangles each of side $10 \,cm$, as shown in figure is $P$. If charge $A, B, C, D, E$ and $F$ are $2\, \mu \,C, 2\, \mu \,C, 2\, \mu \,C,-2\, \mu \,C, -2\, \mu \,C, -2\, \mu \,C$ respectively, then $P$ is :.....$N$

$21.6$

$64.8$

$0$

$43.2$

Solution

The given figure shows force diagram for charge

at $\mathrm{O}$ due to all other charges with $\mathrm{r}=\frac{10}{\sqrt{3}} \mathrm{\,cm}$

$\therefore $ $\mathrm{F}_{\mathrm{net}}=2 \mathrm{F}+4 \mathrm{F} \cos 60^{\circ}=4 \mathrm{\,F}$

$=\frac{4 \mathrm{k}(2\, \mu \mathrm{c})(2\, \mu \mathrm{c})}{\left(\frac{10}{\sqrt{3100}}\right)^{2}}=\frac{4 \times 9 \times 10^{9} \times 2 \times 2 \times 10^{-12}}{\left(\frac{1}{300}\right)}$

$=36 \times 4 \times 300 \times 10^{-3} \mathrm{\,N}$

$=43.2 \mathrm{\,N}$ ( Towards $ \mathrm{E}$)

Standard 12

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Solution

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