Problem 4: Displacement currents. A planar capacitor has two circular plates with equal radii R separated by a distance h. A dielectric cylinder of a smaller radius r < R is inserted co-axially into the center of the capacitor. The dielectric permittivity of the cylinder is €. The voltage between the plates is linearly increased according to V = at. (a) Calculate the magnetic field at the edge of the cylinder. (b) Calculate the magnetic field at the edge of the capacitor. V h حمد

Problem 4: Displacement currents. A planar capacitor has two circular plates with equal radii R separated by a distance h. A dielectric cylinder of a smaller radius r < R is inserted co-axially into the center of the capacitor. The dielectric permittivity of the cylinder is €. The voltage between the plates is linearly increased according to V = at. (a) Calculate the magnetic field at the edge of the cylinder. (b) Calculate the magnetic field at the edge of the capacitor. V h حمد

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Ferromagnetism

Ferromagnetism is a mechanism by which some materials show magnetic properties. Iron and magnetite, an oxide of iron, are two naturally occurring materials that show the property of ferromagnetism. The word ferromagnetism is derived from the Latin name of iron, "Ferrum" as it was the first observed material to show such property. The property of ferromagnetism is shown by only a few substances such as iron, nickel, cobalt, and their alloys. Some transition metals and alloys of rare-earth metals also show ferromagnetism.

Question

**Problem 4: Displacement currents.** A planar capacitor has two circular plates with equal radii \( R \) separated by a distance \( h \). A dielectric cylinder of a smaller radius \( r_c < R \) is inserted coaxially into the center of the capacitor. The dielectric permittivity of the cylinder is \( \epsilon \). The voltage between the plates is linearly increased according to \( V = \alpha t \).

(a) Calculate the magnetic field at the edge of the cylinder.

(b) Calculate the magnetic field at the edge of the capacitor.

**Diagram Explanation:**

The diagram illustrates a side view of the setup. It shows:

- Two circular capacitor plates with radius \( R \) and separation \( h \).
- A dielectric cylinder with radius \( r_c \) centered between the plates.
- The direction marked as \( \hat{z} \), indicating the cylindrical axis along which the capacitor and dielectric are aligned.

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