the distance between two fixed charges 4 meter coulomb and 1 microcoulomb is 10cm. how should a third charge q be placed so that system is in equilibrium

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Solution

Let charge q is placed in between the two charges.
Let x cm be the distance from 4 micro C and (10-x) cm from the 1 micro C.

For an equilibrium condition , net force on the charge q should be zero due to both charges.

Force due to charge = $\frac{k q_{1} q_{2}}{x^{2}}$
therefore,

$\frac{k \times 4 \times 10^{- 6} \times q}{x^{2}} = \frac{k \times 1 \times 10^{- 6} \times q}{{(10 - x)}^{2}} o n s o l v i n g w e g e t, x = 6.66 c m$

So, charge should be placed 6.66 cm form the 4 micro coulomb.

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