- #1

Joseph Rolls

- 9

- 5

- 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

My answers so far are:

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.

:)

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.

:)