# Ranking the force of point charges

1. Sep 22, 2009

### macaco

1. The problem statement, all variables and given/known data

5 point charges;
q1; charge = +q distance = d
q2; charge = +2q distance = 3d
q3; charge = -3q distance = 2d
q4; charge = -4q distance = 3d
q5; charge = -5q distance = 2d
are placed in the vicinity of an insulating spherical shell with a charge (+Q), distributed uniformly over its surface.
Rank the point charges in order of the increasing magnitude of force exerted on them by the sphere. Indicate all ties where appropriate. Show all calculations of force.

2. Relevant equations

Coulomb's law;
F= K (q1)(q2)
---------​
r^2​

3. The attempt at a solution
I've applied coulomb's law to each of the charges, substituting each of the values in;

q1=> F= K Qq
-----​
d^2​

q2=> F= K 2Qq
------​
3d^2​

q3=> F= K -3Qq
------​
4d^2​

q4=> F= K -4Qq
------​
9d^2​

q5=> F= K -5Qq
-------​
4d^2​

I'm still not sure how to rank the equations after I've substituted the values?
I.e.- How do I tell which is higher when I have no numerical value for each?

should I be solving the equations somehow?

Any help much appreciated

2. Sep 23, 2009

### tiny-tim

Hi macaco!

(try using the X2 tag just above the Reply box )

This is really messy, and almost unreadable …

do everything as a factor of qQ/d2

and forget the signs (the + or -) … they're only asking for the magnitudes, so it doesn't matter.

3. Sep 23, 2009

### macaco

You're a legend Tiny Tim.
(The legend of Tiny Tim; sounds like a good book title =P)

Didn't think of taking out a common factor.

The charges in ascending order, according to the values left would be;
q2=> 0.66
q1=> 1
q4=> 1.33
q3=> 1.5
q5=> 2.5

(hopefully)

Thanks again TT

=]

4. Sep 23, 2009

### macaco

The one thing I did not understand, is why you would not use the negative symbols, and rank the negatives below the positives?

5. Sep 24, 2009

### tiny-tim

Hi macaco!

(just got up :zzz: …)
Because the question specified …
and the definition of "magnitude" is that you're only interested in the size, not the direction …

so the magnitude of a negative number -x is x, the magnitude of a vector (such as force) is its length, and the magnitude of a complex number a + ib = re is √(a2 + b2) = r.

6. Sep 24, 2009

### macaco

thanks again TT