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Displacement Current

Displacement Current

Ampère's law, in its usual form, does not work in places where the current changes with time and is not steady. Thus, Maxwell suggested including an additional contribution, called the displacement current, Id, to the real conduction current I.

Significance of Displacement Current

Significance of Displacement Current

A displacement current is analogous to a real current in Ampère's law, participating in Ampère's law the same way as the usual conduction current. However, it is produced by a changing electric field. Displacement current is defined in terms of a time-varying electric field, and also has an associated displacement current density. By adding a term accounting for displacement current, Maxwell modified the existing Ampère's law, which is now called generalized Ampère's law.

Double Resonance Techniques: Overview

Double Resonance Techniques: Overview

Double resonance techniques in Nuclear Magnetic Resonance (NMR) spectroscopy involve the simultaneous application of two different frequencies or radiofrequency pulses to manipulate and observe two distinct nuclear spins. One important application of double resonance is spin decoupling, which selectively suppresses coupling with one type of nucleus while observing the NMR signal from another nucleus, simplifying the spectrum and enhancing resolution.
Spin decoupling is usually achieved by...

Ampere-Maxwell's Law: Problem-Solving

Ampere-Maxwell's Law: Problem-Solving

A parallel-plate capacitor with capacitance C, whose plates have area A and separation distance d, is connected to a resistor R and a battery of voltage V. The current starts to flow at t = 0. What is the displacement current between the capacitor plates at time t? From the properties of the capacitor, what is the corresponding real current?
To solve the problem, we can use the equations from the analysis of an RC circuit and Maxwell's version of Ampère's law.
For the first part of the problem,...

Difference from Background: Limit of Detection

Difference from Background: Limit of Detection

The limit of detection (LOD) is the smallest amount of analyte that can be distinguished from the background noise. The LOD value corresponds to the concentration at which the analyte signal is three times larger than the standard deviation of the blank signal. Below this value, the analyte signal cannot be differentiated from the background noise. It is calculated by dividing the calibration slope by 3 times the standard deviation of the blank signals.
The LOD indicates the presence or absence...

Mass Analyzers: Common Types

Mass Analyzers: Common Types

The quadrupole mass analyzer consists of four cylindrical metal rods arranged in a diamond carrying a DC voltage and a radio-frequency AC voltage. The motion of ions through the quadrupole depends on the field strength, causing only ions of a certain m/z to resonate successfully and strike the detector at a given field strength. Though the transmission rate for these analyzers is high, the exact elemental composition of the sample is not determined because of low resolution; however, they are...

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Related Experiment Video

Updated: Jul 11, 2026

A Random-displacement Measurement by Combining a Magnetic Scale and Two Fiber Bragg Gratings

A Random-displacement Measurement by Combining a Magnetic Scale and Two Fiber Bragg Gratings

Published on: September 30, 2019

Displacement detection with a vibrating rf superconducting interference device: beating the standard linear limit.

Eyal Buks¹, Stav Zaitsev, Eran Segev

¹Department of Electrical Engineering, Technion, Haifa 32000, Israel.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|October 13, 2007

Summary

This study demonstrates a novel displacement detector using coupled nanomechanical and superconducting resonators. Operating in a nonlinear regime enhances displacement sensitivity beyond linear limits, but reduces bandwidth.

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Fabrication and Characterization of Superconducting Resonators

Fabrication and Characterization of Superconducting Resonators

Published on: May 21, 2016

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Last Updated: Jul 11, 2026

A Random-displacement Measurement by Combining a Magnetic Scale and Two Fiber Bragg Gratings

A Random-displacement Measurement by Combining a Magnetic Scale and Two Fiber Bragg Gratings

Published on: September 30, 2019

Fabrication and Characterization of Superconducting Resonators

Fabrication and Characterization of Superconducting Resonators

Published on: May 21, 2016

Area of Science:

Quantum optics
Nanomechanical systems
Superconducting circuits

Background:

Displacement detection is crucial for sensitive measurements in various scientific fields.
Superconducting quantum interference devices (SQUIDs) and resonators offer pathways for high-precision sensing.
Nonlinear dynamics in quantum systems can lead to unique phenomena like noise squeezing.

Purpose of the Study:

To investigate a novel displacement detector configuration.
To analyze the impact of nonlinear resonator oscillations on displacement sensitivity.
To explore noise squeezing and bandwidth limitations in the nonlinear regime.

Main Methods:

Coupling a nanomechanical resonator to a radio frequency superconducting interference device and a superconducting stripline resonator.
Employing adiabatic and rotating wave approximations for sensitivity calculations.
Driving the stripline resonator into nonlinear oscillation and utilizing homodyne detection.

Main Results:

The displacement sensitivity in the nonlinear regime can surpass the linear operating limit.
Noise squeezing is observed in the output signal within the nonlinear regime.
High displacement sensitivity is correlated with a reduced system response time, limiting bandwidth.

Conclusions:

The studied configuration offers enhanced displacement sensitivity through nonlinear operation.
Noise squeezing provides a mechanism for improved signal-to-noise ratio.
A trade-off exists between sensitivity and bandwidth, necessitating careful system design for specific applications.