Electric field on axis of a charged ring

[bennyngreal]

A line charge of uniform charge density lambda forms a circle of radius b that lies in the x-y plane with its centre at the origin.
a)Find the electric field E at the point (0,0,h).
b)At what value of h will E in parta) be a maximum?What is this maximum?

ans:
a)E=人hb/(2e0(h^2+b^2)^1/2 >k(direction of K)
b)h=b/2^1/2 ; Emax=人/(3^3/2*e0*b)

 

[jdwood983]

If you have the answers, what is the problem?

 

[bennyngreal]

the method how to do it

 

[jdwood983]

I think using the equation for an electric field due to a line charge is a good place to start:

$$\mathbf{E}(\mathbf{r})=\frac{1}{4\pi\varepsilon_0}\int_\mathcal{P}\frac{\lambda(\mathbf{r}')}{\mathcal{R}^2}\hat{\mathbf{\mathcal{R}}}dl'$$

Fortunately for you, the line charge is of a uniform density, so this can be reduced to

$$\mathbf{E}(\mathbf{r})=\frac{\lambda}{4\pi\varepsilon_0}\int_\mathcal{P}\frac{1}{\mathcal{R}^2}\hat{\mathbf{\mathcal{R}}}dl'$$

What can you tell me about $\mathcal{R}$--the separation length--and $\hat{\mathbf{\mathcal{R}}}$--the separation vector?