A current i flows into (and, on the other side, out of) a parallel-plate capacitor. The plates are circular, spaced 0.0010 m apart, and have an area of 0.785 m². The voltage across the capacitor changes at 1.0 kV/s, causing a magnetic field to be induced in the capacitor, parallel to the plates. (a) Find the rate at which the electric field and the electric flux are changing between the plates. (b) Find the magnitude of the magnetic field between the plates at a radius of 0.15 m from the axis. (c) Find the magnitudes of the magnetic field at a radius of 1.5 m from the axis. (d) Sketch the magnetic field lines in the region between the plates (at equally spaced magnetic field values) and outside the plates. (e) What is the current i that is flowing into the capacitor? (Calculate this from the rate at which the electric field is changing, and from that the rate at which charge accumulates.)

A current i flows into (and, on the other side, out of) a parallel-plate capacitor. The plates are circular, spaced 0.0010 m apart, and have an area of 0.785 m². The voltage across the capacitor changes at 1.0 kV/s, causing a magnetic field to be induced in the capacitor, parallel to the plates. (a) Find the rate at which the electric field and the electric flux are changing between the plates. (b) Find the magnitude of the magnetic field between the plates at a radius of 0.15 m from the axis. (c) Find the magnitudes of the magnetic field at a radius of 1.5 m from the axis. (d) Sketch the magnetic field lines in the region between the plates (at equally spaced magnetic field values) and outside the plates. (e) What is the current i that is flowing into the capacitor? (Calculate this from the rate at which the electric field is changing, and from that the rate at which charge accumulates.)

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 7
A current i flows into (and, on the other side, out of) a parallel-plate capacitor. The plates are
circular, spaced 0.0010 m apart, and have an area of 0.785 m². The voltage across the capacitor
changes at 1.0 kV/s, causing a magnetic field to be induced in the capacitor, parallel to the plates.
(a) Find the rate at which the electric field and the electric flux are changing between the plates.
(b) Find the magnitude of the magnetic field between the plates at a radius of 0.15 m from the axis.
(c) Find the magnitudes of the magnetic field at a radius of 1.5 m from the axis.
(d) Sketch the magnetic field lines in the region between the plates (at equally spaced magnetic field
values) and outside the plates.
(e) What is the current i that is flowing into the capacitor? (Calculate this from the rate at which
the electric field is changing, and from that the rate at which charge accumulates.)

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Step 1: Given that:

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Step 2: a) Rate of change of electric field and electric flux:

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Step 3: b) Magnitude of magnetic field between the plates at r=0.15 m

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Step 4: (c) Magnitude of magnetic field at r=1.50 m

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Step 5: (d) Graph of magnetic field:

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Step 6: (e) Current flowing into the capacitor:

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