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A thin half ring of radius 35 cm is uniformly charged with a total charge of $$Q$$ coulomb. If the magnitude of the electric field at centre of the half ring is 100 V/m, then the value of $$Q$$ is _______ nC.
$$(\varepsilon_0 = 8.85 \times 10^{-12}$$ C$$^2$$/Nm$$^2$$ and $$\pi = 3.14)$$
$$E = \frac{2k\lambda}{R}$$
$$E = \frac{2kQ}{\pi R^2} = \frac{Q}{2\pi^2\varepsilon_0 R^2}$$
$$100 = \frac{Q}{2 \times (3.14)^2 \times (8.85 \times 10^{-12}) \times (0.35)^2}$$
$$Q \approx 213.79 \times 10^{-12} \text{ C}$$
$$Q \approx 213.79 \times 10^{-3} \text{ nC} \approx 2.14 \text{ nC}$$
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