Work on a charged particle due to Ring

[dwstrait]

Homework Statement

A ring of diameter 7.90 cm is fixed in place and carries a charge of 5.90 $$\mu$$C uniformly spread over its circumference. How much work does it take to move a tiny 3.80 $$\mu$$C charged ball of mass 1.90 g from very far away to the center of the ring? Also, What is the maximum speed it will reach?

Homework Equations

W = -$$\Delta$$U
U(r) = (kqq₀)/r
KE + PE = 0

The Attempt at a Solution

In order to get the work it takes to move the particle, I figured I could find the change in the Potential Energy. The potential energy when the particle is very far away is zero. Is there a better way to approach the problem than using PE?

In order to find velocity_f, I can just use conservation of energy and solve for velocity. So, KE_f = sqrt{-2PE_f/m}

 

[Delphi51]

This looks like quite a difficult problem. Unless you have a potential formula designed for rings, you will have to use integration to sum the contributions to potential from all the point charges dq on the ring.

 

[Delphi51]

Oh, no need to integrate because the point you are interested in is equally distant from all of the charge! Sorry I misled you - not a difficult problem at all!

I don't understand the second part, maximum speed. Surely that just depends on how it is pushed?

 

[dwstrait]

Thanks for suggesting that I didn't need to integrate. I was stuck trying to work out an integral, but once I saw I didn't need one, the problem was very simple.

For the maximum speed, I just solved KE + PE = 0 for velocity, and that was correct.

 

[K29]

I have a similar problem, and I get the right answer without integrating, which is great! But that confuses me. There is a whole section(Halliday and Resnik 8th Extended Edition, page 587- The Electric Field Due To A Line Of Charge) that details on how to integrate to get the electric field at a point P, at a distance, z, from the ring. Why do I need to integrate to get the electric field at a point positioned somewhere in front of the ring, yet I don't have to if I want the potential on a particle at the same point.

(by the way I hope I'm not breaking a rule by posting this here, but it seemed to be pretty pointless starting a new thread and explaining the problem again.)

 

[ideasrule]

Maybe I'm missing something, but if the title of the section is "the electric field due to a line of charge", shouldn't the section talk about lines of charge instead of rings? You don't need to integrate to find the electric field along the axis of a ring. You also don't need integration for finding the field due to a line of charge.

 

[rl.bhat]

I have a similar problem, and I get the right answer without integrating, which is great! But that confuses me. There is a whole section(Halliday and Resnik 8th Extended Edition, page 587- The Electric Field Due To A Line Of Charge) that details on how to integrate to get the electric field at a point P, at a distance, z, from the ring. Why do I need to integrate to get the electric field at a point positioned somewhere in front of the ring, yet I don't have to if I want the potential on a particle at the same point.

The different elements of ring produce the electric field at a point having the same magnitude but different direction. Electric field is a vector quantity which you cannot add directly. Whereas the electric potential is a scalar quantity which you can add directly. Therefore we require integration to find the electric field.

 

[K29]

ah thanks. Fundamentals, fundamentals, fundamentals! :)