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Question:
Two small equal point charges of magnitude $q$ are suspended from a common point on the ceiling by insulating mass less strings of equal lengths. They come to equilibrium with each string making angle $\theta$ from the vertical. If the mass of each charge is $m$, then the electrostatic potential at the centre of line joining them will be $\left(\frac{1}{4\pi\,\in_{0}}=k\right).$
Two small equal point charges of magnitude $q$ are suspended from a common point on the ceiling by insulating mass less strings of equal lengths. They come to equilibrium with each string making angle $\theta$ from the vertical. If the mass of each charge is $m$, then the electrostatic potential at the centre of line joining them will be $\left(\frac{1}{4\pi\,\in_{0}}=k\right).$
Updated On: Jul 15, 2024
- $2\sqrt{k\,mg\,tan\,\theta}$
- $\sqrt{k\,mg\,tan\,\theta}$
- $4\sqrt{k\,mg/tan\,\theta}$
- $\sqrt{mg/tan\,\theta}$
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The Correct Option is C
Solution and Explanation
In equilibrium, $Fe = T\, sin\, \theta$
$mg=T\,cos\,\theta$
$tan\,\theta=\frac{F_{e}}{mg}=\frac{q^{2}}{4\pi\,\in_{0}\,x^{2}\times mg}$
$\therefore x=\sqrt{\frac{q^{2}}{4\pi \,\in_{0}\,tan\,\theta\, mg}}$
Electric potential at the centre of the line
$V=\frac{kq}{x/2}+\frac{kq}{x/2}=4 \sqrt{kmg/tan\,\theta}$
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Concepts Used:
Electrostatic Potential
The electrostatic potential is also known as the electric field potential, electric potential, or potential drop is defined as “The amount of work that is done in order to move a unit charge from a reference point to a specific point inside the field without producing an acceleration.”
SI Unit of Electrostatic Potential:
SI unit of electrostatic potential - volt
Other units - statvolt
Symbol of electrostatic potential - V or φ
Dimensional formula - ML2T3I-1
Electric Potential Formula:
The electric potential energy of the system is given by the following formula:
U = 1/(4πεº) × [q1q2/d]
Where q1 and q2 are the two charges that are separated by the distance d.
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