What is the speed of each sphere when they are very far apart?

Question

The four 1.0 g spheres shown in the figure are released simultaneously and allowed to move away from each other.

Four charges are placed in the corners of a square, 1cm apart. All 4 charges have a charge of +10nC.

What is the speed of each sphere when they are very far apart?

Answer 1

The daunting questing is what does it mean "very far apart"?

The force pushing them apart is a vector superposition of force by 3 other charger on the forth


Ft=F1+F2+F3 (vector sum)
F1=F2=F3
Ftx=F(cos(0) + cos(45) + cos (90))
Ftx=F + Fcos(45)

Fty=F(sin(0) + sin(45) + sin (90))
Fty=Fsin(45) + F

F=kq^2/r^2 (we are not out of the woods yet sinceF=f(r) F is a function of distance between them!)

Let's look a t velocity V
V=at
F=ma
a=F/m
so V=(F/m) t ( simple enough ;))

Now let's do some calculus
dF=-2kq^2/r^3

so F= -2kq^2 integral ( 1/r^3dr) [from r1=1cm to r2 =what ever you want]
F= kq^2( 1/r2^2 - 1/r1^2)
If we assume r2 to be very large
F=kq^2(1/r1^2) (exercise in ...)

Now just do the arithmetic...