$(a)\;0.5 m \qquad(b)\; 1 m\qquad(c)\;0.25 m\qquad(d)\;2 m$

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Answer : (b) 1 m

Explanation :

Work done by electric field = Work done against spring

Let $\;W_{E}\;$ be the work done by electric field . Then

$W_{E}=Q\;E\;x$

Work done by spring = - $\large\frac{1}{2}\;k\;x^2$

Therefore $\;Q\;E\;x-\large\frac{1}{2}\;k\;x^2= \bigtriangleup K.E$

For maximum expansion $\;K.E_{final} =0$

But $\;K.E_{initial}=0$

Then $\;\bigtriangleup K. E=0$

Thus $\;Q\;E\;x-\large\frac{1}{2}\;k\;x^2=0$

$x=\large\frac{2QE}{K}$

$x=\large\frac{2\times100\times10^{-6}\times5\times10^{5}}{100}$

$x=1m$

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