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davezhan

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Link to derivation: www.phys.uri.edu/~gerhard/PHY204/tsl36.pdf

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- Thread starter davezhan
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In summary, the area of a ring section is determined by finding the difference between the areas of two concentric circles, one with a radius of a and the other with a radius of a + da. This results in an area of 2*pi*a*da, as da is considered to be an infinitesimal and its square is negligible. This can also be visualized as a rectangle with a length of 2*pi*a and a width of da, which again results in an area of 2*pi*a*da. By using an integral, we can find the exact area rather than just an approximate area.

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davezhan

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Link to derivation: www.phys.uri.edu/~gerhard/PHY204/tsl36.pdf

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berkeman

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davezhan said:

Link to derivation: www.phys.uri.edu/~gerhard/PHY204/tsl36.pdf

How would you write the equation for the area of that ring section? What happens when you simplify what you've written?

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fluidistic

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HallsofIvy

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Here's another way to look at it: Imagine opening that strip up to a "rectangle". It's length is the circumference of the circle, [itex]2\pi a[/itex], and it's width is da. The area of that "rectangle" is "length times width", [itex]2\pi a da[/itex]. I have put "rectangle" in quotes because, of course, you cannot "open up" a circular strip into a rectangle. This is, again, only true in the

If you were to take da to be any finite length, [itex]2\pi a da[/itex] would give you an approximate area, not an exact area. But you can use "da" in an integral to get the exact area.

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davezhan

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Thank you for your help! The above post helped to clarify things tremendously.

The electric field is a physical quantity that describes the force that an electric charge experiences in a given space. It is a vector quantity, meaning it has both magnitude and direction.

A charged disk is a two-dimensional object with a uniform distribution of electric charge on its surface. It can be formed by cutting a charged sphere in half, resulting in two charged disks with opposite charges on their surfaces.

The electric field of a charged disk can be calculated using the formula E = σ/2ε₀, where σ is the surface charge density (charge per unit area) and ε₀ is the permittivity of free space. This formula assumes that the disk has a radius much larger than its thickness.

The electric field of a charged disk points radially outward from the center of the disk if the charge is positive, and radially inward if the charge is negative. This is because the electric field lines are perpendicular to the surface of the disk and point away from positive charges and towards negative charges.

The electric field of a charged disk decreases as distance from the disk increases. This is because the electric field follows an inverse square law, meaning it decreases with the square of the distance from the source charge. As you move further away from the disk, the electric field becomes weaker.

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