# Charged ring, integrate for electric potential

• Loopas
In summary, the problem involves determining the electric potential at points along the x axis for a flat ring with inner radius R1 and outer radius R2, carrying a uniform surface charge density σ. The solution involves splitting the disk into infinitely thin disks and integrating them together to find the potential. The distance is variable, so the solution requires integration. The distance can be defined using a radius and angle. The final solution involves integrating from R1 to R2 using the equation σ/2ε0 * ∫rdr/√(x^2+r^2).
Loopas

## Homework Statement

A flat ring of inner radius R1 and outer radius R2 carries a uniform surface charge density σ. Determine the electric potential at points along the axis (the x axis). [Hint: Try substituting variables.]

V = (kQ)/r

## The Attempt at a Solution

As you can see from my screenshot, I think I've figured it out mostly I'm just stuck on finding the value for r in the above equation. Shouldn't it be something like sqrt(x^2+y^2)? But that can't be the answer because there's no labelled y-axis...

#### Attachments

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Well, you can't calculate the potential directly from the equation since not every point on the disk will be the same distance from a given point along the x axis. Try splitting the disk into thin disks, and then doing an integration.

What exactly do you mean by "thin disks"? Don't I still need to find the distance between the x point and any given slice of charge on the disk?

By thin I mean infinitely thin. With the disk you're using, the distance to the x point is going to vary as you go farther out from the center. You can find an expression for the distance in terms of the x point and the point you go radially outward, but it's going to be variable, so the solution is going to involve integration -- if you just look at an infinitesimally thin disk and find an expression for the potential along its axis, then you can consider the original disk as a collection of these disks, and integrate them all together.

I'm having trouble finding an expression for the distance between any given point on the ring and the x-point, since there doesn't seem to be any variable that defines the distance between the center of the ring and any given piece of charge on the ring.

Not explicitly given in the diagram, but that doesn't mean you can't create your own. You can indentify a ring of charge with a radius, or if you really want to identify any point, a radius and an angle.

Thanks, I was finally able to figure it out, integrating from R1 to R2:

$\frac{σ}{2ε_{0}}$*$\int$$\frac{rdr}{\sqrt{x^2+r^2}}$

## 1. What is a charged ring?

A charged ring is a theoretical model in physics that represents a circular object with a uniform distribution of electric charge. It can be used to study the behavior of electric fields and potentials in a two-dimensional system.

## 2. How is the electric potential of a charged ring calculated?

The electric potential of a charged ring can be calculated using the integral formula V = kQ/r, where k is the Coulomb constant, Q is the total charge of the ring, and r is the distance from the center of the ring to the point where the potential is being calculated.

## 3. What is the relationship between electric potential and electric field for a charged ring?

The electric potential and electric field for a charged ring have an inverse relationship. This means that where the electric potential is high, the electric field is low, and vice versa. The electric field can be calculated using the formula E = V/r, where V is the electric potential and r is the distance from the center of the ring.

## 4. Can the electric potential of a charged ring be negative?

Yes, the electric potential of a charged ring can be negative. This occurs when the total charge of the ring is negative, or when the distance from the center of the ring is greater than the radius of the ring. A negative electric potential indicates that the electric field is pointing towards the ring.

## 5. In what units is the electric potential of a charged ring measured?

The electric potential of a charged ring is typically measured in volts (V). However, it can also be measured in other units such as joules per coulomb (J/C) or newtons per coulomb (N/C), as it is a measure of the amount of energy per unit charge at a specific point in space.

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