• Support PF! Buy your school textbooks, materials and every day products Here!

Qualitative physics questions.

  • Thread starter aaronmilk3
  • Start date
  • #1
12
0
Derive your results algebraically… No graphical results.
An excess charge of +Q is distributed into two unequal parts, one having charge +q .
Assume that these two new charges are now separated by a non-zero distance. What value of q maximizes the repulsive electric force that one of these new charges exerts on the other?


I got so far that q and the other one is charged (Q-q) due to the repulsive force. I know I would need to take the derivative but this is where I got lost. Any help would be great! Thank you in advance!
 

Answers and Replies

  • #2
collinsmark
Homework Helper
Gold Member
2,894
1,232
I got so far that q and the other one is charged (Q-q) due to the repulsive force. I know I would need to take the derivative but this is where I got lost. Any help would be great! Thank you in advance!
You're on the right track. As a matter of fact, it sounds to me like you almost have it already! :smile:

So go ahead and set up your force equation, with one charge q and the other charge (Q - q), separated by some distance.

To maximize a function, take the derivative with respect to whatever variable you wish to vary, and then set the result equal to zero. Solve for the variable (algebra). That's the value of the variable that maximizes or minimizes the function.*

*The answer can give local maxima or local minima. So if you get multiple values (such as in a quadratic), you might wish to do some sanity checking to figure out what each value is. In this particular problem though, you end up with a single maximum (no minimum) so the need for sanity checking doesn't apply here.

The idea behind the procedure is this: When a smooth function rises to the top of its [possibly local] maximum or bottom of its [possibly local] minimum, the slope of the line is zero at this point. So the above procedure is merely finding where the slope of the function equals zero, as the variable changes.
 
  • #3
supratim1
Gold Member
279
1
yes, right, take the derivative with respect to q (that is d/dq), and solve as above.

you should get Q = q/2
 

Related Threads on Qualitative physics questions.

  • Last Post
Replies
4
Views
4K
  • Last Post
Replies
3
Views
702
Replies
2
Views
2K
Replies
2
Views
5K
Replies
3
Views
1K
Replies
7
Views
453
  • Last Post
Replies
1
Views
562
Replies
7
Views
1K
Replies
3
Views
10K
Replies
1
Views
1K
Top