In the solution part b, I dont understand where the(1/4)^(1/3) is coming from an

Question

In the solution part b, I dont understand where the(1/4)^(1/3) is coming from and also why is there an x multiplyingto it??? This question is the next part to problem 54. In the previousproblem we computed the value of q. That value came out to be± 2.4 x 10^-8 C. But in this problem 55 part b, they are asking to findthe new equilibrium separation x, using the given values of L and mand the computed calue of q. Please tell me how to do it bu showing me all the steps forproblem 55 part b. because the given solution is skippingsteps. Thanks In the solution part b, I dont understand where the(1/4)^(1/3) is coming from and also why is there an x multiplyingto it??? This question is the next part to problem 54. In the previousproblem we computed the value of q. That value came out to be± 2.4 x 10^-8 C. But in this problem 55 part b, they are asking to findthe new equilibrium separation x, using the given values of L and mand the computed calue of q. Please tell me how to do it bu showing me all the steps forproblem 55 part b. because the given solution is skippingsteps. Thanks

Explanation / Answer

Given :
   A redistribution of the remaining charge wouldthen occur,         witheach of the balls getting q/2. Then they would again be        separateddue to electrostatic repulsion, whichresults in the         newequilibrium separation         witheach of the balls getting q/2. Then they would again be        separateddue to electrostatic repulsion, whichresults in the         newequilibrium separation     X' = [ ((q/2)2.L) /(20.mg)]1/3
         ( since x =(q2.L) / (20.mg) )         = [(1/2)2 ]1/3 . x         = (1/4 )1/3. x       = (1/4)1/3 .(5 cm)                  = 3.1 Cm.                  = 3.1 Cm. I hope it helps you

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