Electric Field due to a Ring of Charge

[DarkWarrior]

I've been stuck on this problem for awhile now..

At what distance along the central axis of a ring of radius R and uniform charge is the magnitude of the electric field due to the ring's charge maximum?

Now, I know that the equation for this problem is E = [k|qz|] / [(z^2+R^2)^3/2], which is the electric field magnitude of a charged ring. And to get the maximum, you have to find where the first derivative of the equation where it equals zero.

But when I take the derivative of the equation, I get a complete mess not even close to the answer. Can anyone give me some hints or a push in the right direction? Is my thinking incorrect? Thanks. :)

 

[neutrino]

It's a straighforward problem, and your approcah is right. If you could just post your work, we can try to help you out.

 

[DarkWarrior]

Thanks, confirming that I was going in the right direction was all I needed. I eventually did get the answer, but with some difficultly thanks to my poor algebra skills. :)

 

[goteamusa]

In this problem we do not know E and we are looking for z correct? I do not know how to deal with this problem of having two unknowns. I am given R but that is all.

 

[rwisz]

Hi there,

It seems like you are on the right track with finding the maximum electric field due to a ring of charge. However, it is important to remember that the electric field is a vector quantity, so the magnitude alone may not give you the full picture.

To find the maximum electric field, you can use the equation E = [k|qz|] / [(z^2+R^2)^3/2] and take the derivative with respect to z. This will give you a function for the derivative of the electric field with respect to z.

Next, set this derivative equal to zero and solve for z. This will give you the location along the central axis where the electric field is maximum. You can then plug this value of z back into the original equation to find the maximum electric field magnitude.

If you are still having trouble, it may be helpful to review the concept of taking derivatives and solving for maximum or minimum values. You can also try using an online graphing calculator to plot the derivative function and visually see where it crosses the x-axis, indicating a maximum or minimum point.

I hope this helps and good luck with your problem!