A capacitor is made from two hollow, coaxial copper...

A capacitor is made from two hollow, coaxial copper cylinders, one inside the other. There is air in the space between the cylinders. The inner cylinder has net positive charge and the outer cylinder has net negative charge. The inner cylinder has radius $2.50 \mathrm{mm},$ the outer cylinder has radius $3.10 \mathrm{mm},$ and the length of each cylinder is 36.0 $\mathrm{cm} .$ If the potential difference between the surfaces of the two cylinders is $80.0 \mathrm{V},$ what is the magnitude of the electric field at a point between the two cylinders that is a distance of 2.80 $\mathrm{mm}$ from their common axis and midway between the ends of the cylinders?

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Relationship Between Electric Field and Electric Potential

The electric potential difference between two points is defined as the negative integral of the electric field along the path connecting those points. Understanding this relationship is key in problems where the potential difference is given, as it allows one to determine the electric field profile by differentiating or by setting up an appropriate integral that connects the two quantities.

Gauss’s Law

Gauss's Law relates the electric flux through a closed surface to the charge enclosed by that surface. In systems with high symmetry, such as cylindrical symmetry, Gauss’s Law provides an efficient means of calculating the electric field, as it converts an integration problem into a simpler algebraic one by considering a well-chosen Gaussian surface.

Cylindrical Symmetry

Cylindrical symmetry is a property of systems where physical quantities do not change when rotated around a central axis and are uniform along the length of the cylinder. This symmetry simplifies calculations of electric fields and potentials because it allows the use of cylindrical coordinates and makes it possible to assume that the field depends only on the radial distance from the axis.

Transcript

Please give Ace some feedback