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BITSAT 2021 Paper

Section: Physics

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Question : 32 of 150

Marks: +1, -0

A charge Q is placed at each of the opposite corners of a square. A charge q is placed at each of the other two corners. If the net electrical force on Q is zero, then

\frac{Q}{q}

$-1$
1
$-\frac{1}{\sqrt{2}}$
$-2 \sqrt{2}$

Solution:

It is given that

\vec{F}_A + \vec{F}_B + \vec{F}_D = 0

Where

\vec{F}_A, \vec{F}_B

and

\vec{F}_D

are the forces applied by charges placed at A, B and D on the charge placed at

C

.

\Rightarrow \vec{F}_B + \vec{F}_D = -\vec{F}_A

\left|\vec{F}_B + \vec{F}_D\right| = \sqrt{2} \frac{KqQ}{a^2}

⇒

\left|\vec{F}_A\right| = \frac{KQ^2}{2 a^2}

∴

\sqrt{2} \frac{KqQ}{a^2} = -\frac{KQ^2}{2 a^2}

\Rightarrow \frac{Q}{q} = -2 \sqrt{2}

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