# Magnetoresistance and the Corbino disk

• Joseph Rolls
In summary: They might want you to calculate the emf from that work, but I'm not sure.In summary, the conversation discusses the equations J=I/(2*pi*r*t), u=J/ne=I/(2*pi*r*t*n*e), and F=IB/(2*pi*r*t*n) in theta direction (polar coordinates), as well as applying them to a scenario involving a rod moving through a magnetic field. The group is stuck and unsure of how to proceed, but one idea is to calculate the work done by the azimuthal component of the magnetic force for a full circle and use that to find the emf.
Joseph Rolls
Homework Statement
Magnetoresistance refers to the direct action of a magnetic field on an electric
current. An example of magnetoresistance can be studied using a Corbino disc (see
figure) consisting of a conducting annulus with electrodes on its inner and outer
rims.
Consider an annular disk with thickness 􏱣 , inner radius 􏱒 outer radius 􏱦 and
conductivity 􏱧 and free charge density 􏱔. A battery connected to the rim electrodes
produces a radial current 􏱙􏰬 flowing from the inner boundary to the outer periphery of the disk. A uniform
magnetic
field 􏱘, constant in time, is applied perpendicular to the plane of the annulus.
(a) Prior to the application of the magnetic field, what is the current density in the disc as a function of radial distance 􏰦 from the centre of the disc?
(b) What is the drift velocity of the electrons in the disc?
(c) What is the magnetic force on these electrons?
(d) Write down an expression for the ‘motional emf’ induced at a distance 􏰦 from the centre of the disc?
(e) Write down an expression for the circular current induced in the disc in terms of parameters defined
above and fundamental constants.
Relevant Equations
J=I/A
J=nqu
F=qv x B

a) J=I/(2*pi*r*t)
b) u=J/ne=I/(2*pi*r*t*n*e)
c) F=IB/(2*pi*r*t*n), in theta direction (polar coordinates)
d) This is where I am stuck.
I understand the example for motional emf with a rod moving through a magnetic field but I'm not sure how to apply it to this scenario.
Do we find the work done by the force moving an electron in a full circle round the annulus and get emf from there or something like that?

Any ideas would be greatly appreciated.
:)

Delta2
Joseph Rolls said:

a) J=I/(2*pi*r*t)
OK
b) u=J/ne=I/(2*pi*r*t*n*e)
This would be the drift velocity before B is applied. After B is applied, the drift velocity ##\vec u## will have both a radial component ##u_r## and an azimuthal component ##u_{\theta}##.

They might want you to find expressions for ##u_r## and ##u_{\theta}##.

c) F=IB/(2*pi*r*t*n), in theta direction (polar coordinates)
I don't think this is correct. The magnetic force will have both radial and azimuthal components.
d) This is where I am stuck.
I understand the example for motional emf with a rod moving through a magnetic field but I'm not sure how to apply it to this scenario.
Do we find the work done by the force moving an electron in a full circle round the annulus and get emf from there or something like that?
I'm not sure what they want here. But your interpretation that it's the work done by the azimuthal component of the magnetic force for a full circle sounds good to me.

Joseph Rolls

## 1. What is magnetoresistance?

Magnetoresistance is a phenomenon where the resistance of a material changes in the presence of a magnetic field. This change in resistance can be either positive or negative, depending on the material and the strength of the magnetic field.

## 2. What is a Corbino disk?

A Corbino disk is a circular sample of a material that is used to measure its magnetoresistance. It consists of a central electrode surrounded by a circular ring electrode, with the material sample placed between them.

## 3. How does the Corbino disk measure magnetoresistance?

The Corbino disk measures magnetoresistance by passing an electrical current through the central electrode and measuring the voltage across the outer ring electrode. As the magnetic field is changed, the resistance of the material sample will also change, causing a change in the measured voltage.

## 4. What are some applications of magnetoresistance and the Corbino disk?

Magnetoresistance and the Corbino disk have various applications in fields such as electronics, materials science, and geophysics. They are used to study the magnetic properties of materials, measure small changes in magnetic fields, and develop new magnetic sensors and devices.

## 5. What factors can affect the accuracy of magnetoresistance measurements using the Corbino disk?

The accuracy of magnetoresistance measurements using the Corbino disk can be affected by factors such as the quality and uniformity of the material sample, the strength and direction of the magnetic field, and any external noise or interference. It is important to carefully control these factors to obtain accurate and reliable results.

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