Electric Field Problem II

  • Thread starter bodensee9
  • Start date
  • #1
178
0
Hello:

I have the following. A stationary ring of radius a lies in the yz plane and has a uniform positive charge Q. A small particle that has mass m and a negative charge -q is located at the center of the ring. (a) show that is x << a the electric field along the axis of the ring is porportional to x. (b) find the force on teh particle as a function of x. (c) show that if the particle is given a small displacement in the +x direction, it will perform SHM.

So for (a), do I do, since the E for a ring is k*Q*x/(a^2+x^2)^(3/2), where x is the displacement on the z axis, and a is the radius. So that's a because if x is very small then the equation is basically k*Q*x/a^3. So this is porportional to x.

(b) Then wouldn't the force just be q*E, and since there's a negative charge -q here, wouldn't the F = q*k*Q*x/a^3?

(c) So to show SHM, I need to show that acceleration = some constant w^2*displacement. So couldn't I just set q*k*Q/a^3 as w?

Thanks!!
 

Answers and Replies

  • #2
Defennder
Homework Helper
2,591
5
Your answer for (a) is correct provided you got the expression for E correct (I didn't check it). (b) is odd since x=0 and it is evident by symmetry that that E-field at the centre of the ring where the particle is located is clearly 0. Unless they mean (if the particle was instead placed at some x=b), then you would have to perform the integration to get the value.

(c) is nearly correct. Just note you have to take the mass of particle into consideration. Be careful of the missing square.
 
  • #3
178
0
THanks!
 

Related Threads on Electric Field Problem II

  • Last Post
Replies
4
Views
7K
  • Last Post
Replies
9
Views
1K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
0
Views
2K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
0
Views
1K
  • Last Post
Replies
7
Views
815
  • Last Post
Replies
1
Views
6K
  • Last Post
Replies
5
Views
3K
  • Last Post
2
Replies
31
Views
2K
Top