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Презентация на тему Currents in мetals

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Lecture 11Currents in MetalsThe effects of magnetic fields. The production and properties of magnetic fields.
Physics 1Voronkov Vladimir Vasilyevich Lecture 11Currents in MetalsThe effects of magnetic fields. The production and properties of magnetic fields. Types of ConductivityConductors are materials through which charge moves easily. Insulators are Drift speed of electronsThere is a zigzag motion of an electron in So when we consider electric current as a flow of electrons:	in reality Current in metalsEvery atom in the metallic crystal gives up one or ResistivityA conductor with current:Current density:I – electric currentA – the cross-sectional area ConductivityA current density J and an electric field E are established in Ohm’s law againFor many materials (including most metals), the ratio of the MagnetsA single magnetic pole has never been isolated. Magnetic poles are always Magnet PolesMagnet field lines connect unlike poles.Magnet field lines repels from like poles. Magnet ForceThe magnitude FB of the magnetic force exerted on the particle The text in the previous slide can be summarized as:So the units Direction of FBRight hand rule:	The fingers point in the direction of v, Magnetic field directionMagnetic field lines coming out of the paper are indicated Magnetic Force on a CurrentMagnetic force is exerted on a single charge n is the number density of charged particles qvd is the drift Arbitrary shaped wireThe force on a small segment of an arbitrary shaped as B is uniform:The magnetic force on a curved current-carrying wire in So, the force on a straight wire in a uniform magnetic field Loop Wire in a Uniform Magnetic fieldThe net magnetic force acting on Current Loop Torque in a Uniform Magnetic Field- Overhead view of a When the magnetic field is 				parallel to the plane of the 				loop, When the loop is not 						parallel to the 							magnetic field, i.e. the In formula for torque					 						we have vector A: 					 - Its Right – hand rule for loop				The	direction of the 					magnetic moment is the Magnetic MomentThe vector product IA is defined to be the magnetic dipole Potential Energy of a Magnetic MomentThe potential energy of a system having Motion of a Charged Particle in a Uniform Magnetic Field											When the velocity Using the obtained formula					 we get the angular velocityhere v is perpendicular to B. Lorentz ForceIn the presence of E and B, the force acting on The Hall EffectWhen a current-carrying conductor is placed in a magnetic field, the magnetic force 						       exerted Using that A=td – cross sectional area of the conductor,t – thickness When the charge carriers in a Hall-effect apparatus are negative, the upper Units in SiMagnetic field			B  T= N*s/(C*m)							   T= N/(A*m)Electric Field			E
Слайды презентации

Слайд 2 Lecture 11
Currents in Metals
The effects of magnetic fields.

Lecture 11Currents in MetalsThe effects of magnetic fields. The production and properties of magnetic fields.


The production and properties of magnetic fields.


Слайд 3 Types of Conductivity
Conductors are materials through which charge

Types of ConductivityConductors are materials through which charge moves easily. Insulators

moves easily.
Insulators are materials through which charge does

not move easily.
Semiconductors are materials intermediate to conductors and insulators.

Слайд 4 Drift speed of electrons





There is a zigzag motion

Drift speed of electronsThere is a zigzag motion of an electron

of an electron in a conductor. The changes in

direction are the result of collisions between the electron and atoms in the conductor. The net motion – drift speed of the electron is opposite the direction of the electric field.

Слайд 5 So when we consider electric current as a

So when we consider electric current as a flow of electrons:	in

flow of electrons:



in reality there happens zigzag motion of

free electrons in the metal:

Слайд 6 Current in metals
Every atom in the metallic crystal

Current in metalsEvery atom in the metallic crystal gives up one

gives up one or more of its outer electrons.

These electrons are then free to move through the crystal, colliding at intervals with stationary positive ions, then the resistivity is:
ρ = m/(ne2τ)
n - the number density of free electrons,
m and e – mass and charge of electron,
– average time between collisions.

Слайд 7 Resistivity
A conductor with current:

Current density:

I – electric current
A

ResistivityA conductor with current:Current density:I – electric currentA – the cross-sectional

– the cross-sectional area of the conductor
vd – drift

speed
E = ρJ
ρ - resistivity

Слайд 8 Conductivity
A current density J and an electric field

ConductivityA current density J and an electric field E are established

E are established in a conductor whenever a potential

difference is maintained across the conductor:


σ is conductivity:
σ = 1/ ρ.

Слайд 9 Ohm’s law again
For many materials (including most metals),

Ohm’s law againFor many materials (including most metals), the ratio of

the ratio of the current density to the electric

field is a constant σ that is independent of the electric field producing the current:
J = σE

Слайд 10 Magnets
A single magnetic pole has never been isolated.

MagnetsA single magnetic pole has never been isolated. Magnetic poles are

Magnetic poles are always found in pairs.
The direction of

magnetic field is from the North pole to the South pole of a magnet.

Слайд 11 Magnet Poles
Magnet field lines connect unlike poles.


Magnet field

Magnet PolesMagnet field lines connect unlike poles.Magnet field lines repels from like poles.

lines repels from like poles.


Слайд 12 Magnet Force
The magnitude FB of the magnetic force

Magnet ForceThe magnitude FB of the magnetic force exerted on the

exerted on the particle is proportional to the charge

q and to the speed v of the particle.
The magnitude and direction of FB depend on the velocity of the particle and on the magnitude and direction of the magnetic field B.
When a charged particle moves parallel to the magnetic field vector, the magnetic force acting on the particle is zero.
When the particle’s velocity vector makes any angle Θ≠0 with the magnetic field, the magnetic force acts in a direction perpendicular to both v and B.
The magnetic force exerted on a positive charge is in the direction opposite the direction of the magnetic force exerted on a negative charge moving in the same direction.
The magnitude of the magnetic force exerted on the moving particle is proportional to sin Θ, where Θ is the angle the particle’s velocity vector makes with the direction of B.

Слайд 13
The text in the previous slide can be

The text in the previous slide can be summarized as:So the

summarized as:




So the units for B are:

The magnetic force is perpendicular to both v and B.
FB=qVBsinΘ

Слайд 14 Direction of FB
Right hand rule:
The fingers point in

Direction of FBRight hand rule:	The fingers point in the direction of

the direction of v, with B coming out of

your palm, so that you can curl your fingers in the direction of B. The direction of , and the force on a positive charge, is the direction in which the thumb points.

Слайд 15 Magnetic field direction
Magnetic field lines coming out of

Magnetic field directionMagnetic field lines coming out of the paper are

the paper are indicated by dots, representing the tips

of arrows coming outward.

Magnetic field lines going into the paper are indicated by crosses, representing the feathers of arrows going inward.

Слайд 16 Magnetic Force on a Current
Magnetic force is exerted

Magnetic Force on a CurrentMagnetic force is exerted on a single

on a single charge moving in a magnetic field.

A current-carrying wire also experiences a force when placed in a magnetic field. This follows from the fact that the current is a collection of many charged particles in motion; hence, the resultant force exerted by the field on the wire is the vector sum of the individual forces exerted on all the charges making up the current. The force exerted on the particles is transmitted to the wire when the particles collide with the atoms making up the wire.

Слайд 17 n is the number density of charged particles

n is the number density of charged particles qvd is the

q
vd is the drift speed of q
A – area

of the segment
L – the length of the segment
Then AL is the volume of the segment, and

nAL is the number of charged particles q.
Then the net force acting on all moving charges is:


Слайд 18 Arbitrary shaped wire
The force on a small segment

Arbitrary shaped wireThe force on a small segment of an arbitrary

of an arbitrary shaped wire is:

The total force is:


a

and b are the end points of the wire.


Слайд 19 as B is uniform:




The magnetic force on a

as B is uniform:The magnetic force on a curved current-carrying wire

curved current-carrying wire in a uniform magnetic field is

equal to that on a straight wire connecting the end points and carrying the same current.

Curved Wire in a Uniform Magnetic field


Слайд 20 So, the force on a straight wire in

So, the force on a straight wire in a uniform magnetic

a uniform magnetic field is:


is a vector multiplication.
Where L is a vector that points in the direction of the current I and has a magnitude equal to the length L of the segment. This expression applies only to a straight segment of wire in a uniform magnetic field.

Magnetic force on a straight wire


Слайд 21 Loop Wire in a Uniform Magnetic field
The net

Loop Wire in a Uniform Magnetic fieldThe net magnetic force acting

magnetic force acting on any closed current loop in

a uniform magnetic field is zero:



Then the net force is zero:
FB=0

Слайд 22 Current Loop Torque in a Uniform Magnetic Field
-

Current Loop Torque in a Uniform Magnetic Field- Overhead view of

Overhead view of a rectangular loop in a uniform

magnetic field.
Sides 1 and 3 are parallel to magnetic field, so only sides 2 and for experiences magnetic forces.
- Magnet forces, acting on sides 2 and 4 create a torque on the loop.


Слайд 23 When the magnetic field is parallel to the

When the magnetic field is 				parallel to the plane of the

plane of the loop, the maximal torque on the

loop is:


ab is the area of the loop A:


Слайд 24 When the loop is not parallel to the

When the loop is not 						parallel to the 							magnetic field, i.e.

magnetic field, i.e. the angle between A and B

is Θ < 90° then:





So the torque on a loop in a uniform magnetic field is:

This formula is correct not only for a rectangular loop, but for a planar loop of any shape.

Слайд 25 In formula for torque
we have vector

In formula for torque					 						we have vector A: 					 -

A:
- Its direction is perpendicular

to the plane of the loop,
- its magnitude is equal to the area of the loop.

We determine the direction of A using the right-hand rule. When you curl the fingers of your right hand in the direction of the current in the loop, your thumb points in the direction of A.

Area Vector


Слайд 26 Right – hand rule for loop
The direction of the

Right – hand rule for loop				The	direction of the 					magnetic moment is

magnetic moment is the same as the direction of

A.

Слайд 27 Magnetic Moment
The vector product IA is defined to

Magnetic MomentThe vector product IA is defined to be the magnetic

be the magnetic dipole moment μ (often simply called

the “magnetic moment”) of the current loop:


Then the torque on a current-carrying loop is:

Слайд 28 Potential Energy of a Magnetic Moment
The potential energy

Potential Energy of a Magnetic MomentThe potential energy of a system

of a system having magnetic dipole μ in the

magnetic field B is:


Here we have scalar product μ B. Then the lowest energy is when μ points as B, the highest energy is when μ points opposite B:

Слайд 29 Motion of a Charged Particle in a Uniform

Motion of a Charged Particle in a Uniform Magnetic Field											When the

Magnetic Field




When the velocity of a charged particle is

perpendicular to a uniform magnetic field, the particle moves in a circular path in a plane perpendicular to B. The magnetic force FB acting on the charge is always directed toward the center of the circle.

Слайд 30
Using the obtained formula



we get the angular

Using the obtained formula					 we get the angular velocityhere v is perpendicular to B.

velocity


here v is perpendicular to B.


Слайд 31 Lorentz Force
In the presence of E and B,

Lorentz ForceIn the presence of E and B, the force acting

the force acting on a charged particle is:

here q

is the charge of the particle,
v – the speed of the particle,
E – electric field vector
B – magnetic field vector


Слайд 32 The Hall Effect
When a current-carrying conductor is placed

The Hall EffectWhen a current-carrying conductor is placed in a magnetic

in a magnetic field, a potential difference is generated

in a direction perpendicular to both the current and the magnetic field.

Слайд 33 the magnetic force

the magnetic force 						    exerted on the

exerted on the carriers

has magnitude qvdB.
this force is balanced by the electric force qEH:



d is the width of the conductor:


n – charge density: .vd - charge carrier drift speed.

then we obtain the Hall voltage:

Слайд 34 Using that A=td – cross sectional area of

Using that A=td – cross sectional area of the conductor,t –

the conductor,
t – thickness of the conductor we can

obtain:




RH is the Hall coefficient:

RH = 1/(nq)

Слайд 35 When the charge carriers in a Hall-effect apparatus

When the charge carriers in a Hall-effect apparatus are negative, the

are negative, the upper edge of the conductor becomes

negatively charged, and c is at a lower electric potential than a.

When the charge carriers are positive, the upper edge becomes positively charged, and c is at a higher potential than a.

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