Figure shows a rod ${AB}$, which is bent in a $120^{\circ}$ circular arc of radius $R$. A charge $(-Q)$ is uniformly distributed over rod ${AB}$. What is the electric field $\overrightarrow{{E}}$ at the centre of curvature ${O}$ ?
Figure shows a rod ${AB}$, which is bent in a $120^{\circ}$ circular arc of radius $R$. A charge $(-Q)$ is uniformly distributed over rod ${AB}$. What is the electric field $\overrightarrow{{E}}$ at the centre of curvature ${O}$ ?
- [JEE MAIN 2021]
- A
$\frac{3 \sqrt{3} {Q}}{8 \pi \varepsilon_{0} {R}^{2}}(\hat{{i}})$
- B
$\frac{3 \sqrt{3} Q}{8 \pi^{2} \varepsilon_{0} R^{2}}(\hat{i})$
- C
$\frac{3 \sqrt{3} Q}{16 \pi^{2} \varepsilon_{0} R^{2}}(\hat{i})$
- D
$\frac{3 \sqrt{3} Q}{8 \pi^{2} \varepsilon_{0} R^{2}}(-\hat{i})$
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Five charges, $\mathrm{q}$ each are placed at the corners of a regular pentagon of side $\mathrm{'a'}$ as in figure.
$(a)$ $(i)$ What will be the electric field at $O$, the centre of the pentagon ?
$(ii)$ What will be the electric field at $O$ if the charge from one of the corners (say $A$ $)$ is removed ?
$(iii)$ What will be the electric field at $O $ if the charge $q$ at $A$ is replaced by$ -q$ ?
$(b) $ How would your answer to $(a)$ be affected if pentagon is replaced by $n\,-$ sided regular polygon with charge $q$ at each of its corners ?
Five charges, $\mathrm{q}$ each are placed at the corners of a regular pentagon of side $\mathrm{'a'}$ as in figure.
$(a)$ $(i)$ What will be the electric field at $O$, the centre of the pentagon ?
$(ii)$ What will be the electric field at $O$ if the charge from one of the corners (say $A$ $)$ is removed ?
$(iii)$ What will be the electric field at $O $ if the charge $q$ at $A$ is replaced by$ -q$ ?
$(b) $ How would your answer to $(a)$ be affected if pentagon is replaced by $n\,-$ sided regular polygon with charge $q$ at each of its corners ?
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Find the electric field at point $P$ (as shown in figure) on the perpendicular bisector of a uniformly charged thin wire of length $L$ carrying a charge $Q.$ The distance of the point $P$ from the centre of the rod is $a=\frac{\sqrt{3}}{2} L$.
Find the electric field at point $P$ (as shown in figure) on the perpendicular bisector of a uniformly charged thin wire of length $L$ carrying a charge $Q.$ The distance of the point $P$ from the centre of the rod is $a=\frac{\sqrt{3}}{2} L$.
- [JEE MAIN 2021]