Electric Potential within coaxial cylinder

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In summary, the problem involves a long metal cylinder with radius a supported on an insulating stand and a long, hollow metal tube with radius b. There is a positive charge per unit length on the inner cylinder and an equal negative charge per unit length on the outer cylinder. The potential for r < a is calculated using the equation [(lambda)/(2(pi)(epsilon))]*[ln(b/a)]. The reference point is b and the integration is done from b to a because the potential inside the smaller cylinder is constant, as there is no electric field inside a conductor at equilibrium. The smaller cylinder is not a conductor and is supported on an insulating stand.
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Homework Statement

A long metal cylinder with radius a is supported on an insulating stand on the axis of a long, hollow metal tube with radius b. Thew positive charge per unit length on the inner cylinder is $$\lambda$$, and there is an equal negative charge per unit length on the outer cylinder. Calculate the potential for r < a; a < r < b; r > b.

Homework Equations

EA=q/epsilon
Va - Vb = $$\int$$E.dl

The Attempt at a Solution

I really just need help figuring out why the answer for when r < a is:
[(lambda)/(2(pi)(epsilon))]*[ln(b/a)]
The reference point here is b. If we are looking for the potential INSIDE the smaller cylinder with radius a, then why are we only integrating from b to a? Shouldn't it be from b to 0? Or is the potential inside the smaller cylinder constant? Why would that be?

Last edited:
Or is the potential inside the smaller cylinder constant? Why would that be?

Well what IS the potential inside a hollow conductor at equilibrium? The electric field is zero, right? so...

The smaller cylinder is not hollow and I don't think its a conductor (and its supported on an insulating stand anyway)... unless being "metal" is synonymous with conductor? E inside a conductor is 0, but I don't think the smaller cylinder is a conductor.

1. What is electric potential within a coaxial cylinder?

The electric potential within a coaxial cylinder is the amount of electric potential energy per unit charge at a specific point within the cylinder. It is a measure of the strength of the electric field at that point.

2. How is electric potential within a coaxial cylinder calculated?

The electric potential within a coaxial cylinder can be calculated using the formula V = kQ/ln(b/a), where V is the electric potential, k is the Coulomb constant, Q is the charge on the inner cylinder, and b and a are the radii of the outer and inner cylinders, respectively.

3. What factors affect the electric potential within a coaxial cylinder?

The electric potential within a coaxial cylinder is affected by the charge on the inner cylinder, the distance between the cylinders, and the radii of the outer and inner cylinders. It is also affected by the dielectric constant of the material between the cylinders.

4. How does the electric potential within a coaxial cylinder change with distance?

The electric potential within a coaxial cylinder decreases as the distance from the inner cylinder increases. This is because the electric field strength decreases with distance according to the inverse square law.

5. What is the significance of the electric potential within a coaxial cylinder?

The electric potential within a coaxial cylinder is important in understanding the behavior of electric fields and charges within the cylinder. It can also be used to calculate the work done on a charge moving between the cylinders, which is useful in many practical applications such as in capacitors and transmission lines.

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