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  • A point charge q is placed at the centre of a uniformly charge ring of total charge Q. Two small pieces, each with charge q' are removed from the ring as shown in the figure. The net force on t

A point charge q is placed at the centre of a uniformly charge ring of total charge Q. Two small pieces, each with charge q' are removed from the ring as shown in the figure. The net force on the charge q due to the remaining ring.

Option: 1

\frac{1}{4 \pi \epsilon_0} \frac{q q^{\prime}}{R^2}


Option: 2

\sqrt2\times\frac{1}{4 \pi \epsilon_0} \frac{q q^{\prime}}{R^2}


Option: 3

2\sqrt2\frac{1}{4 \pi \epsilon_0} \frac{q q^{\prime}}{R^2}


Option: 4

\sqrt2\frac{3}{4 \pi \epsilon_0} \frac{q q^{\prime}}{R^2}


Answers (1)

best_answer

If \vec{F}_1 is force due to remaining ring and \vec{F}_2 and \vec{F}_3 by the removed charges then-

\begin{aligned} \vec{F}_1+\vec{F}_2 & +\vec{F}_3=0 \\ \vec{F}_1 & =-\left(\vec{F}_2+\vec{F}_3\right) \\ \vec{F}_1 & =\sqrt{F_2^2+F_3^2}=\sqrt{F^2+F^2} \\ & =\sqrt{2 F^2} \\ F_1 & =\sqrt{2} F=\sqrt{2} \times \frac{1}{4 \pi \epsilon_2} \frac{q q^{\prime}}{R^2} \end{aligned}

Posted by

Deependra Verma

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