Electrostatics Question 694
Two identical blocks are kept on a frictionless horizontal table connected by a spring of stiffness k and of original length $ l _{0}. $ A total charge Q is distributed along the spring at equilibrium of equal to x. Value of Q is
Options:
A) $ 2{\ell _{0}}\sqrt{4\pi {\varepsilon _{0}}k( {\ell _{0}}+x )} $
B) $ 2x\sqrt{4\pi {\varepsilon _{0}}k( {\ell _{0}}+x )} $
C) $ 2( {\ell _{0}}+x )\sqrt{4\pi {\varepsilon _{0}}kx} $
D) $ ( {\ell _{0}}+x )\sqrt{4\pi {\varepsilon _{0}}kx} $
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Answer:
Correct Answer: C
Solution:
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}}{{{( {\ell _{0}}+x )}^{2}}}=kx\text{ }Q=2( {\ell _{0}}+x )\sqrt{4\pi {\varepsilon _{0}}kx}. $
BETA
