High School Confused about this force calulation in Resnick Halliday Krane Electrostatics

[KnightTheConqueror]

TL;DR

Resnick Halliday Krane Electrostatics Sample Problem 25-7 doubt

I'm confused in the calculation for R/2. The author took in account that the charge will change by a factor 1/8. But how does it show that the coloumbic force will become 1/8th. The distance will also reduce by half shouldn't that also be taken into account? Or am I missing something here?

 

[kuruman]

TL;DR Summary: Resnick Halliday Krane Electrostatics Sample Problem 25-7 doubt

I'm confused in the calculation for R/2. The author took in account that the charge will change by a factor 1/8. But how does it show that the coloumbic force will become 1/8th. The distance will also reduce by half shouldn't that also be taken into account? Or am I missing something here?View attachment 336703

Been there, done that. You are correct and the book is wrong. See discussion here.
https://www.physicsforums.com/threa...rted-on-an-electron-inside-a-nucleus.1052346/

 

[Ibix]

I agree with you - they've correctly calculated the charge ratio and forgotten the distance ratio.

Edit: beaten to it, I see.

 

[PeroK]

 

[KnightTheConqueror]

Been there, done that. You are correct and the book is wrong. See discussion here.
https://www.physicsforums.com/threa...rted-on-an-electron-inside-a-nucleus.1052346/

Thank you, i just started electromagnetism and i got disappointed that perhaps I'm not getting proper grasp of the concepts. Thanks for clarifying the book is wrong

 

[kuruman]

Thank you, i just started electromagnetism and i got disappointed that perhaps I'm not getting proper grasp of the concepts. Thanks for clarifying the book is wrong

I wish you success with your studies. If you need more help, you know where to find it.