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Three equal charges each +Q, placed at the corners of on equilateral triangle of side what will be the force on any charge \left ( k=\frac{1}{4\pi \varepsilon _{0}} \right )

  • Option 1)

    \frac{kQ^{2}}{a^{2}}\;

  • Option 2)

    \; \; \frac{2kQ^{2}}{a^{2}}\;

  • Option 3)

    \; \frac{\sqrt{2}kQ^{2}}{a^{2}}\; \;

  • Option 4)

    \; \frac{\sqrt{3}kQ^{2}}{a^{2}}

 

Answers (1)

best_answer

As we learned

Direction -

\tan \alpha =\frac{F_{2}\sin \Theta }{F_{1}+F_{2}\cos \Theta }

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 Suppose net force is to be calculated on the charge which is kept at A. Two charges kept at B and C are applying force on that particular charge, with direction as shown in the figure.

\\*Since\; F_{b}=F_{c}=F=k\frac{Q^{2}}{a^{2}}\\*So,\, F_{net}=\sqrt{F_{B}^{2}+F_{C}^{2}+2F_{B}F_{C}\cos 60}\\*F_{net}=\sqrt{3}F=\frac{\sqrt{3}kQ^{2}}{a^{2}}

 


Option 1)

\frac{kQ^{2}}{a^{2}}\;

Option 2)

\; \; \frac{2kQ^{2}}{a^{2}}\;

Option 3)

\; \frac{\sqrt{2}kQ^{2}}{a^{2}}\; \;

Option 4)

\; \frac{\sqrt{3}kQ^{2}}{a^{2}}

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prateek

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