Location of maximum electric field due to a ring of charge?

[mHo2]

Homework Statement

Hi,
Having some trouble with answering this question:
A thin nonconducting rod with a uniform distribution of +'ve charge 'Q' is bent into a circle of radius R. There is an axis, 'z' which originates in the center of this ring.

In terms of 'R', at what +'ve value of z is that magnitude maximum?

I'm not precisely sure what this question is asking (slightly ambiguous), however I'm assuming it's asking where the electric field due to this ring is at a maximum. Any help is appreciated!

Homework Equations

E = (q*z*K)/(Z^2 + R^2)^(3/2)
E = F/Q
Where K = 1/(4*Pi*E(naught))

The Attempt at a Solution

I have determined z in terms of R to be
z = R/Tan(Pi/2 - Theta)

Where 'Theta is the angle of elevation between the 'point' on z and the edge of the ring.

Thanks!

 

[Mindscrape]

Looks as though the problem wants you to find the electric field on the axis of the ring. So you will want the charge distribution (hint: make the circle into a line to get charge per length), and you will want to employ symmetry. Is this a class that uses calculus? If so set up the integral and I, or someone else, will tell you if it's right.

 

[mHo2]

Looks as though the problem wants you to find the electric field on the axis of the ring. So you will want the charge distribution (hint: make the circle into a line to get charge per length), and you will want to employ symmetry. Is this a class that uses calculus? If so set up the integral and I, or someone else, will tell you if it's right.

It kind of does, however the magnitude of the z components is zero when it lies between the ring.

 

[SammyS]

Homework Statement

Hi,
Having some trouble with answering this question:
A thin nonconducting rod with a uniform distribution of +'ve charge 'Q' is bent into a circle of radius R. There is an axis, 'z' which originates in the center of this ring.

In terms of 'R', at what +'ve value of z is that magnitude maximum?

I'm not precisely sure what this question is asking (slightly ambiguous), however I'm assuming it's asking where the electric field due to this ring is at a maximum. Any help is appreciated!

Homework Equations

E = (q*z*K)/(Z^2 + R^2)^(3/2)
E = F/Q
Where K = 1/(4*Pi*E(naught))

The Attempt at a Solution

I have determined z in terms of R to be
z = R/Tan(Pi/2 - Theta)

Where 'Theta is the angle of elevation between the 'point' on z and the edge of the ring.

Thanks!

So, the ring of charge lies in the xy coordinate plane, and is centered at the origin.

I assume you have determined the E field at any point along the z-axis.

I general, how do you find the maximum of a function?

 

[Mindscrape]

It kind of does, however the magnitude of the z components is zero when it lies between the ring.

No, you have to find the field for all points along the z-axis and then maximize the function you get for the E-field. Maybe it's zero, maybe it's not. :p What did you get, and how did you get it?

 

[mHo2]

No, you have to find the field for all points along the z-axis and then maximize the function you get for the E-field. Maybe it's zero, maybe it's not. :p What did you get, and how did you get it?

Yes, but I can't seem to simplify the equation I get.

 

[Mindscrape]

So, take the equation
$$dE=\frac{\lambda dl}{r^2}$$
and use symmetry/geometry to tell me what this equation (differential form of Coulomb's law) becomes in terms of your parameters and coordinates.