Calculating Electric Field and Potential of a Charged Ring Segment

[Octavius1287]

Hi everyone, i have been looking at this problem for a few days now and i am pretty stuck, ill explain why

first the problem :
a charge Q is distributed over a ring section of radius r, between angles 90 and 180. find the V and E at the origin.

Now the problem I am having ais everything that is kind of similar to this problem or about charged rings is only for uniformly charged rings and i can't find anything about just a segment, and in those cases i think E at the center is 0. Also every where i look I am seeing a different formula for E of a charged ring. I am pretty confused

 

[Octavius1287]

i also don't understand how only one segment and in this case the 2nd quadrant can be charged..

 

[sandy.bridge]

$$\vec{E}=\int\frac{\lambda\hat{r}}{r^2}ds$$
Where $\lambda$ merely represents the charge distribution $Q$, and $\hat{r}$ represents a unit vector perpendicular to each segment pointing towards the origin. You want to take the line integral on the interval $(\pi/2, \pi)$.

Normally, the electric field would be zero in the center of a circle with uniform charge distribution. However, it is not in this instance.

 

[Octavius1287]

thank you, what source did you get that equation from id like to read more about it

 

[Octavius1287]

i see 1/4*pi*eo and to the power of 3/2 in a lot of ring equations that's was confusing me is the difference between those and this one

 

[sandy.bridge]

Not entirely sure what level you are at, but this was in both my vector calculus and electrostatics textbook. You may find variations depending on how the charge is distributed (line, surface, etc).

 

[Octavius1287]

College, and the one in my Electromagnetics book is

E=$\hat{z}$[h/(4$\pi$ε0(b^2+h^2)^3/2)]*Q where b is the radius and h is the height, but like i said its for a uniform charge

 

[dlgoff]

College, and the one in my Electromagnetics book is

E=$\hat{z}$[h/(4$\pi$ε0(b^2+h^2)^3/2)]*Q where b is the radius and h is the height, but like i said its for a uniform charge

This is probably what it's referring to.

I don't know if this will be helpful, but take a look.

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elelin.html

Regards

 

[Octavius1287]

ya all those make sense to me, but i read that page and once again it said it was only for a uniform charge

 

[dlgoff]

... i read that page and once again it said it was only for a uniform charge

Yes.

...problem :
a charge Q is distributed over a ring section of radius r, between angles 90 and 180.

This doesn't mean it is NON-uniform for the rest of the ring. Aren't they looking for the field from the contribution of charge on just this piece of the ring?

If so,

...You want to take the line integral on the interval $(\pi/2, \pi)$.