Cylindrical capacitor
A cylindrical capacitor is two coaxial conductive cylinders separated by a dielectric. In Principles of Physics II, it models how geometry and material control capacitance and electric field storage.
What is cylindrical capacitor?
A cylindrical capacitor in Principles of Physics II is a capacitor made from two coaxial cylinders, one inside the other, with an insulating dielectric between them. Instead of flat plates, the charge sits on curved surfaces, and the electric field fills the space between the cylinders.
The key idea is that the inner cylinder and outer cylinder hold equal and opposite charge when the capacitor is charged. That separation of charge creates an electric field directed radially outward from the inner conductor to the outer conductor. The field is not something you see directly, but it is what stores the electric potential energy.
Because the geometry is cylindrical, the field strength changes with distance from the center. That is different from the nearly uniform field between parallel plates. In an ideal cylindrical capacitor, the field depends on the radius, the length of the cylinders, and the dielectric material. For a long capacitor with inner radius a and outer radius b, the capacitance is C = 2πϵL / ln(b/a). This tells you that capacitance increases with length L and with dielectric permittivity ϵ, but decreases when the radii are spaced farther apart in a way that increases ln(b/a).
The dielectric matters because it lowers the electric field for a given charge compared with vacuum, which lets the capacitor store more charge at the same voltage. In a physics class, that is the bridge between the geometry of the device and the energy stored in the electric field.
You will usually treat a cylindrical capacitor as an idealized model when the cylinders are long compared with the gap between them. That assumption lets you ignore edge effects at the ends, where the field starts to curve and the simple formula becomes less exact. So when you solve problems, the main job is to recognize the geometry, apply Gauss's law or the capacitance formula, and connect the result back to charge, voltage, and stored energy.
Why cylindrical capacitor matters in Principles of Physics II
Cylindrical capacitors show how capacitance is not just about having two conductors, it is about the shape of the conductors and the material between them. In Principles of Physics II, that makes them a clean example of how electric fields store energy and how geometry changes the math.
This term also connects the chapter on capacitors to the bigger electromagnetism toolkit. When you use Gauss's law to find the field between cylinders, you are practicing the same reasoning that shows up in other symmetric charge distributions. Then you carry that field into potential difference and capacitance.
The concept matters any time a problem asks you to compare capacitor designs. A cylindrical capacitor can pack a lot of capacitance into a compact shape, so it is a nice contrast with parallel-plate and spherical geometries. Seeing why the logarithm appears in the formula helps you understand why spacing and radius ratios affect the result the way they do.
It also gives you a more physical feel for what capacitance means. Instead of memorizing that C is charge divided by voltage, you see how the electric field, dielectric, and shape of the conductor pair determine how much charge can be stored for a given applied potential difference.
Keep studying Principles of Physics II Unit 3
Official unit cheatsheet
open one-pagerHow cylindrical capacitor connects across the course
Capacitance
Cylindrical capacitors are one geometry used to define capacitance. Once you know the field between the cylinders, you can connect charge, voltage, and stored energy through C = Q/V. This makes the term a good bridge from the general definition of capacitance to a specific, solvable setup.
Dielectric
The dielectric between the cylinders changes the electric field and raises the capacitance compared with vacuum. In problems, you may see the permittivity written as ϵ = κϵ0, so a larger κ means more charge can be stored for the same applied voltage. That is why material choice matters.
Electric Field
The field inside a cylindrical capacitor is radial and depends on distance from the axis, so it is not uniform like the field between ideal parallel plates. If you can sketch the field lines and describe their direction, you are already partway to solving the capacitance problem.
Capacitor Network
A cylindrical capacitor may appear as one element inside a larger circuit or as part of a network of capacitors. Even if the geometry is unusual, the circuit rules still apply, so you may need to combine it with other capacitors using series or parallel ideas after finding its capacitance.
Is cylindrical capacitor on the Principles of Physics II exam?
A problem set or quiz question will usually give you the inner radius, outer radius, length, and dielectric constant, then ask for capacitance, stored charge, or potential difference. The move is to identify the geometry as cylindrical, choose the correct formula, and keep your units consistent with meters and farads.
You may also be asked to reason from the field instead of plugging straight into the formula. In that case, sketch the radial electric field, apply the idea that the field is stronger closer to the inner cylinder, and explain why the logarithm shows up in the final result. If the prompt compares two designs, focus on how changing radius, length, or dielectric changes the capacitance rather than just restating the definition.
If the problem includes energy, connect the capacitor to U = 1/2 CV^2 or U = Q^2/(2C). That lets you move from geometry to stored energy, which is a common physics exam skill.
Cylindrical capacitor vs parallel-plate capacitor
A cylindrical capacitor uses two coaxial cylinders, while a parallel-plate capacitor uses two flat conducting plates. The field shape is different too: cylindrical fields are radial and vary with distance, but ideal parallel-plate fields are nearly uniform between the plates. The formulas reflect that geometry difference.
Key things to remember about cylindrical capacitor
A cylindrical capacitor is two coaxial conducting cylinders separated by a dielectric, with charge stored on the curved surfaces.
Its capacitance depends on geometry and material, with C = 2πϵL / ln(b/a) for an ideal long cylinder.
The electric field between the cylinders is radial, not uniform, and that field is what stores the energy.
A larger dielectric permittivity increases capacitance, while a bigger gap between the cylinders lowers it.
In physics problems, the main skill is to identify the geometry, use the right formula, and connect the result to charge, voltage, and energy.
Frequently asked questions about cylindrical capacitor
What is a cylindrical capacitor in Principles of Physics II?
It is a capacitor made of two concentric cylindrical conductors with a dielectric between them. The charge sits on the inner and outer cylinders, creating a radial electric field in the space between. In Physics II, it is a standard example of how geometry affects capacitance.
How do you find the capacitance of a cylindrical capacitor?
For an ideal long cylindrical capacitor, use C = 2πϵL / ln(b/a), where a is the inner radius, b is the outer radius, and L is the length. The dielectric permittivity ϵ tells you how the material changes the stored charge for a given voltage. If the problem changes the material, update ϵ before solving.
Is the electric field inside a cylindrical capacitor uniform?
No. The field is radial and changes with distance from the center, so it is stronger near the inner cylinder and weaker near the outer cylinder. That is one of the biggest differences from the ideal parallel-plate capacitor, where the field is usually treated as uniform.
Why does a dielectric increase capacitance in a cylindrical capacitor?
The dielectric reduces the effective electric field for the same amount of charge, which lowers the potential difference needed to store that charge. Since capacitance is C = Q/V, a smaller V for the same Q means a larger capacitance. The material matters just as much as the shape.