ElectrostaticsMedium
Question
Six-point charges are kept $60^{\circ}$ apart from each other on the circumference of a circle of radius R as shown in figure. The net electric field at the centre of the circle is $\_\_\_\_$ .
( $\epsilon_{o}$ is permittivity of free space)
Options
A.$- \frac{5Q}{8\pi\epsilon_{o}R^{2}}(\widehat{i} + \sqrt{3}\widehat{j})$
B.$- \frac{Q}{4\pi \in_{o}R^{2}}(\sqrt{3}\widehat{i} - \widehat{j})$
C.$- \left( \frac{5Q}{8\pi\epsilon_{o}R^{2}} \right)(\widehat{i} - 3\widehat{j})$
D.$\frac{Q}{4\pi\epsilon_{o}R^{2}}(\sqrt{3}\widehat{i} - \widehat{j})$
Solution
Let $\frac{KQ}{r^{2}} = E_{0}$
$${{\overrightarrow{E}}_{\text{net~}} = 2E_{0}cos30^{\circ}( - \widehat{i}) + 2E_{0}sin30^{\circ}(\widehat{j}) }{= \frac{2kQ}{r^{2}}\left\lbrack \frac{\sqrt{3}}{2}( - \widehat{i}) + \frac{1}{2}\widehat{j} \right\rbrack }{= \frac{- 1Q}{4\pi\varepsilon_{0}r^{2}}(\sqrt{3}\widehat{i} - \widehat{j})}$$
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