A) \[2{{\ell }_{0}}\sqrt{4\pi {{\varepsilon }_{0}}k\left( {{\ell }_{0}}+x \right)}\]
B) \[2x\sqrt{4\pi {{\varepsilon }_{0}}k\left( {{\ell }_{0}}+x \right)}\]
C) \[2\left( {{\ell }_{0}}+x \right)\sqrt{4\pi {{\varepsilon }_{0}}kx}\]
D) \[\left( {{\ell }_{0}}+x \right)\sqrt{4\pi {{\varepsilon }_{0}}kx}\]
Correct Answer: C
Solution :
[c] For maximum elongation charges on the blocks must be equal to 0/2 on each block. \[\therefore \frac{1}{4\pi {{\varepsilon }_{0}}}\frac{\frac{Q}{2}\frac{Q}{2}}{{{\left( {{\ell }_{0}}+x \right)}^{2}}}=kx\text{ }Q=2\left( {{\ell }_{0}}+x \right)\sqrt{4\pi {{\varepsilon }_{0}}kx}.\]
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