A cylindrical capacitor consists of two coaxial cylindrical conductors. The capacitance of a cylindrical capacitor depends on the radii of the inner and outer cylinders and the length of the capacitor. Determining the capacitance involves understanding the electric field between the cylinders and applying Gauss's law.
The capacitance, $C$, of a cylindrical capacitor is given by the formula:
$C = \frac{2 \pi \epsilon_0 L}{\ln(b/a)}$Where:
Match the term with the correct definition:
| Term | Definition |
|---|---|
| 1. Capacitance | A. The ratio of charge to potential difference. |
| 2. Permittivity | B. A measure of how easily an electric field can permeate a medium. |
| 3. Electric Field | C. A region around a charged particle or object within which a force would be exerted on other charged particles or objects. |
| 4. Potential Difference | D. The work done per unit charge to move a test charge between two points. |
| 5. Coaxial | E. Having a common axis. |
A cylindrical capacitor consists of two ________ cylinders. The ________ of the capacitor depends on the ________ of the inner and outer cylinders, as well as the ________. The formula to calculate capacitance is $C = \frac{2 \pi \epsilon_0 L}{\ln(b/a)}$, where $\epsilon_0$ is the ________ of free space.
How does increasing the length of a cylindrical capacitor affect its capacitance, assuming all other parameters remain constant? Explain the physical reason behind this effect.
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