How to get maximum electrostatic force?

  • Thread starter catch22
  • Start date
  • #1
62
0

Homework Statement


Let's take two spheres that are somewhat nearby. On one sphere, sphere A, there is Q units of charge. Now, we take some little bit of charge q off of sphere A, and put it on sphere B. What should the ratio q/Q be if we want the electrostatic force between the spheres to be a maximum?

Homework Equations


F = K Q q / r2

The Attempt at a Solution


[/B]
For this question, I just took plotted numbers and found that the charge q has to be half of Q in order to have the greatest electrostatic force between the spheres. So the ratio of q/Q = 1/2

How would one do this problem without plotting numbers?
 

Answers and Replies

  • #2
BvU
Science Advisor
Homework Helper
14,452
3,742
Hi catch,

Do you know what the criteria are for the maximum of a function of one variable ? If so, all you need to do is write F as a function of one variable !
 
  • #3
62
0
Hi catch,

Do you know what the criteria are for the maximum of a function of one variable ? If so, all you need to do is write F as a function of one variable !
unfortunately, I don't. do you mean like global maximum/minimums of a function?
 
  • #4
BvU
Science Advisor
Homework Helper
14,452
3,742
I mean like if f(x) has a maximum in x0, then what about df/dx at x = x0
 
  • #5
62
0
I mean like if f(x) has a maximum in x0, then what about df/dx at x = x0
oh, so if I picture a graph, the highest point is where the slope is 0.
and to get the slope, we need the derivative.
 
  • #6
BvU
Science Advisor
Homework Helper
14,452
3,742
Yessss! Now, what derivative ? f is easy: F. But what is a candidate for the variable x ?
 
  • #7
62
0
Yessss! Now, what derivative ? f is easy: F. But what is a candidate for the variable x ?
q or Q?
 
  • #8
BvU
Science Advisor
Homework Helper
14,452
3,742
Well, that's a no-brainer: Q is a number, so it must be q ! And now it's time to realize that the Q in the problem statement is not the Q in the relevant equation ! But you knew that, right ?
 
  • #9
62
0
Well, that's a no-brainer: Q is a number, so it must be q ! And now it's time to realize that the Q in the problem statement is not the Q in the relevant equation ! But you knew that, right ?
whoops, for a second I thought Q was the charge of the sphere that was taking in q.
 
  • #10
BvU
Science Advisor
Homework Helper
14,452
3,742
So what is now the one-variable function you are going to differentiate with respect to ##q## ?
 
  • #11
62
0
So what is now the one-variable function you are going to differentiate with respect to ##q## ?
F = k q Q / r^2
 
  • #13
BvU
Science Advisor
Homework Helper
14,452
3,742
Agreed. Does it work out OK now ?
 
  • #14
62
0
Agreed. Does it work out OK now ?
hmm, my q turned into a 1.
dF / dq = K(Q-1) / r^2 = 0

Q = 1

doesn't seem right.?:)
 
  • #15
BvU
Science Advisor
Homework Helper
14,452
3,742
Ah ! So not the same as when looking at the plotted figure ?
Or perhaps a second try differentiating F = some constant times ( Qq - q2 ) ?
 
  • #16
62
0
Ah ! So not the same as when looking at the plotted figure ?
Or perhaps a second try differentiating F = some constant times ( Qq - q2 ) ?
where did ( Qq - q2 ) come from?
 
  • #17
BvU
Science Advisor
Homework Helper
14,452
3,742
  • #18
62
0
!
oh, we shouldn't have factored out the q?

anyways, k (Q-2q)/ r^2 = 0

Q - 2q = 0

2q = Q

q/Q = 1/2
 
  • #19
BvU
Science Advisor
Homework Helper
14,452
3,742
Bingo ! Well done.
 

Related Threads on How to get maximum electrostatic force?

  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
5
Views
2K
Replies
2
Views
680
  • Last Post
Replies
12
Views
43K
Replies
8
Views
2K
Replies
8
Views
6K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
1
Views
1K
Top