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1. Electric Charges and Fields
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$A$ and $B$ are two identical blocks made of a conducting material. These are placed on a horizontal frictionless table and connected by a light conducting spring of force constant $‘K’$. Unstretched length of the spring is $L_0$. Charge $Q/2$ is given to each block. Consequently, the spring stretches to an equilibrium length $L$. Value of $Q$ is
A
$\sqrt {4\pi {\varepsilon _0}KL} $
B
$L\sqrt {\frac{K}{{4\pi {\varepsilon _0}\left( {L - {L_0}} \right)}}} $
C
$2L\sqrt {4\pi {\varepsilon _0}K\left( {L - {L_0}} \right)} $
D
$4\pi {\varepsilon _0}K\left( {L - {L_0}} \right)$
Solution
$\frac{\frac{1}{4 \pi \varepsilon_{0}}\left(\frac{Q}{2}\right)^{2}}{(L)^{2}}=K\left(L-L_{0}\right)$
$Q=2 L \sqrt{4 \pi \varepsilon_{0} K\left(L-L_{0}\right)}$
Standard 12
Physics
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