Ranking the force of point charges problem

[macaco]

Homework Statement

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.

Homework Equations

Coulomb's law;
F= K (q1)(q2)

---------​

r^2​

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

 

[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.

 

[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

=]

 

[macaco]

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

 

[tiny-tim]

Hi macaco!

(just got up :zzz: …)

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

Because the question specified …

Rank the point charges in order of the increasing magnitude of force …

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^iθ is √(a² + b²) = r.

 

[macaco]

thanks again TT