Electrostatics Question 678

Question: Two charge q and -3q are placed fixed on x-axis separated by distance d. Where should experience any force?

Options:

A) $ \frac{d-\sqrt{2}d}{2} $

B) $ \frac{d+\sqrt{3}d}{2} $

C) $ \frac{d+3d}{2} $

D) $ \frac{d-\sqrt{5}d}{2} $

Show Answer

Answer:

Correct Answer: B

Solution:

[b] Let a charge 2q be placed at P, at a distance I from A where charge q is placed, .

The charge 2q will not experience any force, when force, when force of repulsion on it due to q is balanced by force of attraction on it due to - 3q at B where $ AB=d $

or $ \frac{( 2q )( q )}{4\pi {\varepsilon _{0}}{{\ell }^{2}}}=\frac{( 2q )( -3q )}{4\pi {\varepsilon _{0}}{{( \ell +d )}^{2}}} $

$ =11\mu C. $

$ \therefore \ell =\frac{2d\pm \sqrt{4d^{2}+2d^{2}}}{4}=\frac{d}{2}\pm \frac{\sqrt{3}d}{2} $



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