Electrostatics

JEE Main level, single correct, medium

100 of 311

Question 100 of 311

Figure shows a rod ABAB, which is bent in a 120∘120^{\circ} circular arc of radius RR. A charge(−Q)(-Q) is uniformly distributed over rod ABAB. What is the electric filed E⃗\vec{E} at the centre of curvature OO ?

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Answer: (A) 33Q8π2ϵ0R2i^\dfrac{3\sqrt{3}Q}{8{\pi }^{2}{\epsilon }_{0}{R}^{2}}\hat{i}

δ=2kλRsin⁡θ2i^\delta =\dfrac{2k\lambda }{R}\sin \dfrac{\theta }{2}\hat{i}
=2kR(Q2Rπ3)sin⁡60∘i^=\dfrac{2k}{R}\left(\dfrac{Q}{2R\dfrac{\pi }{3}}\right)\sin 60^{\circ}\hat{i}
=3kQπR232i^=\dfrac{3kQ}{\pi {R}^{2}}\dfrac{\sqrt{3}}{2}\hat{i}
=332πkQR2i^=\dfrac{3\sqrt{3}}{2\pi }\dfrac{kQ}{{R}^{2}}\hat{i}

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