For a cylindrical capacitor with fixed radii, if the length L is doubled, the capacitance:

Study for the Electrostatics Test. Enhance your understanding with interactive questions, detailed explanations, and comprehensive review. Prepare for success!

Multiple Choice

For a cylindrical capacitor with fixed radii, if the length L is doubled, the capacitance:

Explanation:
The key idea is that for a coaxial cylindrical capacitor with fixed radii, capacitance scales directly with length. The formula is C = (2π ε0 L) / ln(b/a), where a and b are the inner and outer radii. With the radii fixed, all factors except L stay constant, so C ∝ L. Doubling the length doubles the capacitance because there is more surface area facing the electric field along the cylinder, allowing more charge to be stored at the same voltage. The other options would require different dependencies on length (1/L, L^2, or independence from L), which don’t apply here.

The key idea is that for a coaxial cylindrical capacitor with fixed radii, capacitance scales directly with length. The formula is C = (2π ε0 L) / ln(b/a), where a and b are the inner and outer radii. With the radii fixed, all factors except L stay constant, so C ∝ L. Doubling the length doubles the capacitance because there is more surface area facing the electric field along the cylinder, allowing more charge to be stored at the same voltage. The other options would require different dependencies on length (1/L, L^2, or independence from L), which don’t apply here.

More Multiple Choice Questions
Subscribe

Get the latest from Passetra

You can unsubscribe at any time. Read our privacy policy