Understanding the Saddle Point in Griffith's CED Problem 3.2

[hasanhabibul]

can anyone pleasezzzz help me by answering elaborately Problem 3.2 ... ...consider the cubical
arrangement of fixed charges in Fig. 3.4. It looks, off hand, as though a positive charge at
the center would be suspended in midair, since it is repelled away from each corner. Where
is the leak in this "electrostatic bottle"?

why answer of this question is saddle point and the midpoint of the each side of the cube ...

 

[hasanhabibul]

i have the solution manual ... i have downloaded it form gigapedia...but in the solution manual it did not describe ...only they had given the answer ...can u explain??

 

[Redbelly98]

If you post the actual question, people who don't own a copy of Griffiths might be able to help.

What is the problem actually asking? You will need to make an attempt at solving it before getting help, by the way.

 

[hasanhabibul]

if u keep six +q charges in the six corner of a cube ...and keep a +q charge suspended in the midair ...then certainly the chage will leak through the cube ...my question is where is the potantial leakage of the cube for the system...

 

[Redbelly98]

Try calculating the potential at the center of the cube. Then you can calculate it at some other locations near the center, and see where the potential becomes lower.

p.s. it's 8 charges at the corners, isn't it?

EDIT: not sure if this is obvious, but you need to write an expression for the potential to get started.