free physics video tutorials for all

 

 

Fields & Effects

 

Magnetic Fields 2

 

Flemming's LH Rule

force on a charged particle

force on a metal conductor

the Hall Effect

 

 

 

Flemming's Left Hand Rule

 

The rule describes the resulting directional motion of a current carrying conductor(or a moving charged positive particle) from the current and field directions.

 

The three quantities FIELD, CURRENT and MOTION are mutually at right angles to each other.

 

 

Flemming's Left Hand Rule

 

 

Using the left hand, position the first finger, second finger and thumb to form the x,y,z axes. The highlighted letters within the words help you remember the three quantities.

 

 

First finger - Field direction

 

seCond finger - Current direction

 

thuMb - Motion produced

 

 

back to top

 

 

Force on a Charged Particle in a Magnetic Field

 

The force on a charged particle moving in a magnetic field is at right angles to the velocity. This causes the particle to perform circular motion.

 

 

charged particle with velocity normal to magnetic  field

 

 

For a velocity at right angles to the field, the magnitude of the force F is simply the product of the magnetic flux density B, the charge Q on the particle and its velocity v.

 

force on a charged particle in a magnetic field - equation #2

 

Equating this force with the centripetal force, we obtain the relation :

 

particle motion in a magnetic field - equation #1

 

Rearranging to make the radius of motion r the subject :

 

particle motion in a magnetic field - equation #1

 

This is quite an important result.

 

The radius r is :

i) directly proportional to the momentum (mv)


ii) inversley proportional to the flux density B


iii) inversley proportional to the charge Q

 

 

Whether a particle orbits clockwise or anticlockwise indicates charge type(+ or -).

 

So with information from orbital radius particles can be identified in nuclear physics experiments.

 

Now consider a particle moving at velocity v at an angle θ to a magnetic field of flux density B.

 

 

particle injected at an angle to a magnetic field

 

 

The velocity v is resolved along the field ( vsinθ ) and at right angles to it ( vcosθ ).

 

This means that the particle performs circular motion with a velocity at right angles to the circle. The result is a corkscrew motion.

 

particle injected at an angle to a magnetic field

 

 

Circular motion velocity is now vsinθ (not v). Therefore the original equation for normal field and velocity is amended to :

 

force on a charged particle in a magnetic field

 

 

back to top

 

 

Force on a Metal Conductor in a Magnetic Field

 

For a metal conductor of length L , carrying a current I , at right angles to a magnetic field of flux density B , the force F upwards on the conductor is simply : (left-hand diagram below)

 

force on a metal conductor normal to a magnetic field - equation #1

 

For a metal conductor at an angle θ to the field, the force upwards on the conductor is : (centre diagram)

 

force on a metal conductor normal to a magnetic field - equation #1

 

For a metal conductor in-line with the field (right-hand diagram) θ = 0o and sine 0o = 0 . Hence the force F is zero.

 

 

force on a rod at an angle to a magnetic field

 

 

The expression force on a metal conductor normal to a magnetic field - equation #1 can be derived from first principles.

 

Consider a metal conductor of length L with electrons travelling along it with an average drift velocity v.


The average time t for an electron to traverse the length L, is :

(using time = distance/velocity)

 

force on a metal conductor - equation #1

 

If Q is the charge transferred along the conductor in time t , then the current I (by definition the charge passes in unit time) is :

 

force on a metal conductor - equation #3

 

The charge Q is a particular number n of electrons :

 

force on a metal conductor - equation #2

 

Substituting for Q and t into the expression for current I :

 

force on a metal conductor - equation #4

 

Quoting the equation for a moving particle at an angle to a magnetic field :

 

force on a charged particle in a magnetic field

 

Substituting for Q : (force on a metal conductor - equation #2 )

 

force on a metal conductor - equation #5

 

rearranging,

 

force on a metal conductor - equation #6

 

Substituting for Nev from above,

 

force on a metal conductor - equation #7

 

 

 

back to top

 

 

The Hall Effect

 

The Hall Effect refers to the potential difference that builds up across opposing faces of a cuboidal shaped material when it is carrying current and placed in a uniform magnetic field.

 

 

hall Effect - diagram #1

 

 

The potential difference V is a consequence of free electrons in the material being deflected by the magnetic field.

 

The electrons move in arcs and build up on the bottom face.

 

Removal of free electrons from the top half of the solid makes the top face positive.

 

The electric field E produced by the deposited electrons is very weak to start with. As more electrons accumulate, it grows stronger.

 

The resultant force on electrons(Bev minus eE) becomes weaker and weaker.

 

Eventually a point is reached when the magnetic and electric forces are equal(Bev = eE) and no more electrons are added.

 

 

Hall Efect - diagram #2

 

 

When this happens the potential difference across the top and bottom faces reaches a maximum (VH).

 

The p.d. is called the Hall Voltage and is a measure of the magnetic field passing through the solid.

 

An expression for the Hall Voltage can be obtained from a consideration of the forces on an electron, when they are balanced.

 

The downward magnetic force F is given by :

 

Hall Effect - equation #1

 

The upward electric force is given by :

 

Hall Effect - equation #2

 

For a uniform electric field,

 

Hall Effect - equation #3

 

where d is the thickness of the sample.

 

 

Substituting for E into the electric force equation,

 

Hall Effect - equation #4

 

Equating the magnetic force with the electric force :

 

Hall Effect - equation #5

 

cancelling the e's and making VH the subject of the equation.

 

Hall Effect - equation #6

 

Quoting the Drift Velocity equation from the site's Electricity section:

(electricity/conduction in metals)

 

Hall Effect - equation #7

 

Rearranging to make the drift velocity v the subject,

 

Hall Effect - equation #7b

 

Now, substituting for v into the equation for VH ,

 

Hall Effect - equation #8

 

The cross-sectional area A of the sample between left and right faces is simply the product of the height d and its thicknes t.

 

Hall Effect equation #9

 

Substituting for A in the new expression for VH ,

 

Hall Effect equation #10

 

Shuffling around bottom terms to make the equation more memorable :

 

Hall Effect equation #11

 

 

The Hall voltage is larger in semiconductors than metals. This is because VH is inversely proportional to the number of charge carriers/unit volume n.

 

Values for n are much smaller in semiconductors. So VH is larger.

 

Typical values of VH for specimens under similar conditions :

 

metals ~ 10-6 V

semiconductors ~ 10-2 V

 

A useful application of the Hall Effect is to test whether a material is p or n-type semiconductor.

 

Note also how Hall Voltage VH is inversely proportional to sample thicknes t.

 

So it follows that a thin sample (a small t) will give a large Hall Voltage.

 

 

 

back to top

 

 

 

this week's promoted video

 

 from Physics Trek

 

 

creative commons license

All downloads are covered by a Creative Commons License.
These are free to download and to share with others provided credit is shown.
Files cannot be altered in any way.
Under no circumstances is content to be used for commercial gain.

 

 

 

 

©copyright a-levelphysicstutor.com 2016 - All Rights Reserved