JEE Mains · Physics · STD 12 - 1. Electric charges and fields
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 __________ .
(\( \epsilon \) is permittivity of free space)
- A \( -\frac{5Q}{8\pi\epsilon_{o}R^{2}}(\hat{i}+\sqrt{3j}) \)
- B \( -\frac{Q}{4\pi\epsilon_{0}R^{2}}(\sqrt{3}\hat{i}-\hat{j}) \)
- C \( -(\frac{5Q}{8\pi\epsilon_{0}R^{2}})(\hat{i}-3\hat{j}) \)
- D \( \frac{Q}{4\pi\epsilon_{0}R^{2}}(\sqrt{3}\hat{i}-\hat{j}) \)
Answer & Solution
Correct Answer
(B) \( -\frac{Q}{4\pi\epsilon_{0}R^{2}}(\sqrt{3}\hat{i}-\hat{j}) \)
Step-by-step Solution
Detailed explanation
Let \( \frac{KQ}{r^{2}}=E_{0} \) \( \vec{E}_{net}=2E_{0}cos~30^{\circ}(-\hat{i})+2E_{0}sin~30^{\circ}(\hat{j}) \) \( =\frac{2kQ}{r^{2}}[\frac{\sqrt{3}}{2}(-\hat{i})+\frac{1}{2}\hat{j}] \) \( =\frac{-1Q}{4\pi\epsilon_{0}{r^{2}}}(\sqrt{3}\hat{i}-\hat{j}) \)
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