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doktorwho

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**1. Homework Statement**

A flat ring, with radii ##b>a## like on the picture is charged with a surface charge density ##ρ_s=ρ_0\frac{b}{r}## where ##ρ_0=const.## Calculate the potential of the ring on the ##z-axis## by taking the reference point to be in the infinity. Picture below.

2. Homework Equations

A flat ring, with radii ##b>a## like on the picture is charged with a surface charge density ##ρ_s=ρ_0\frac{b}{r}## where ##ρ_0=const.## Calculate the potential of the ring on the ##z-axis## by taking the reference point to be in the infinity. Picture below.

2. Homework Equations

Since the reference point is in the infinty the expression for the potential is $$dV=\frac{dQ}{4πε_0r}$$

## The Attempt at a Solution

I have some ideas and have tried to solve the problem but need the confirmation if this is correct or not.

It goes like this.

1) First i calculated the expression for the total charge on the ring: note: (##ρ_l## is the linear charge density on one circle of the ring)

##ρ_l=ρ_sdA=ρ_s*rdθ=ρ_s2rπ##

##dQ=ρ_s2rπdr##

2)Then i wrote the expression for the potential: note: ( ##R## is the distance to some point on the ##z-axis##

##dV=\frac{dQ}{4πε_0R}##

##V=\int_{a}^{b}\frac{ρ_srdr}{2ε_0\sqrt{z^2+r^2}}##

What do you think about this? Is it correct? Is there an easier way?[/B]

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