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Magnetic Field

- A magnetic field is a region in which a body with

magnetic properties experiences a force.

Sources of Magnetic Field

- Magnetic fields are produced by electric

currents, which can be macroscopic currents in

wires, or microscope currents associated with

electrons in atomic orbits.

Magnetic Field Lines

- A magnetic field is visualised using magnetic

lines of force which are imaginary lines such

that the tangent at any point gives the direction

of the magnetic field at that point.

Magnetic Flux Pattern

The Earths Magnetic Field

- The Earth's magnetic field appears to come from a

giant bar magnet, but with its south pole located

up near the Earth's north pole.

Properties of Magnetic Field Lines

- Magnetic lines of force never intersect.
- By convention, magnetic lines of force point from

north to south outside a magnet (and from south

to north inside a magnet). - Field lines converge where the magnetic force is

strong, and spread out where it is weak. (Number

of lines per unit area is proportional to the

magnetic field strength.)

Magnetic flux pattern due to current in a

straight wire at right angles to a uniform field

Net flux is greater on this side of the wire

Net flux is lesser on this side of the wire

Flemings Left Hand Rule

- If you point your left forefinger in the

direction of the magnetic field, and your second

finger in the direction of the current flow, then

your thumb will point naturally in the direction

of the resulting force!

Force on a current-carrying conductor

- The direction of magnetic force always

perpendicular to the direction of the magnetic

field and the direction of current passing

through the conductor.

Magnetic Flux Density

- The magnetic flux density is defined as the force

per unit length per unit current acting on a

current-carrying conductor at right angle to the

field lines.

Unit tesla (T) or gauss (G), 1 G

10-4 T or weber/m2

Typical Values of the magnetic flux density

Magnetic Field Measurements

- Using a current balance (d.c.)
- Using a search coil (a.c.)
- Using a Hall probe (d.c.)

Magnetic flux density due to a straight wire

- Experiments show that the magnetic flux density

at a point near a long straight wire is

r

P ?

- This relationship is valid as long as r, the

perpendicular distance to the wire, is much less

than the distance to the ends of the wire.

Calculation of B near a wire

Where ?o is called the permeability of free

space.

Permeability is a measure of the effect of a

material on the magnetic field by the material.

Magnetic Field due to a Solenoid

- The magnetic field is strongest at the centre of

the solenoid and becomes weaker outside.

Magnetic Flux Density due to a Solenoid

- Experiments show that the magnetic flux density

inside a solenoid is

and

So we have

or

where

Variation of magnetic flux density along the axis

of a solenoid

- B is independent of the shape or area of the

cross-section of the solenoid. - At a point at the end of the solenoid,

Magnetic Flux Density due to Some

Current-carrying conductors(1)

- Circular coil

Where r is the radius of the coil

- Helmholtz coils

Where r is the separation of the coil

Magnetic Flux density due to Some

Current-carrying Conductors (2)

Force on a moving charge in a magnetic field

- The force on a moving charge is proportional to

the component of the magnetic field perpendicular

to the direction of the velocity of the charge

and is in a direction perpendicular to both the

velocity and the field.

http//webphysics.davidson.edu/physlet_resources/b

u_semester2/c12_force.html

Right Hand Rule

- Direction of force on a positive charge given by

the right hand rule.

Free Charging Moving in a Uniform Magnetic Field

- If the motion is exactly at right angles to a

uniform field, the path is turned into a circle.

- In general, with the motion inclined to the

field, the path is helix round the lines of

force.

Mass Spectrometer

- The mass spectrometer is used to measure the

masses of atoms.

- Ions will follow a straight line path in this

region.

- Ions follow a circular path in this region.

Aurora Borealis (Northern Lights)

- Charged ions approach the Earth from the Sun (the

solar wind and are drawn toward the poles,

sometimes causing a phenomenon called the aurora

borealis.

Causes of Aurora Borealis

- The charged particles from the sun approaching

the Earth are captured by the magnetic field of

the Earth. - Such particles follow the field lines toward the

poles. - The high concentration of charged particles

ionizes the air and recombining of electrons with

atoms emits light.

http//www.exploratorium.edu/learning_studio/auror

as/selfguide1.html

Hall Effect

http//maxwell.ucdavis.edu/electro/magnet_force/h

all.html

- When a current carrying conductor is held firmly

in a magnetic field, the field exerts a sideways

force on the charges moving in the conductor. - A buildup of charge at the sides of the conductor

produces a measurable voltage between the two

sides of the conductor.

- The presence of this measurable transverse

voltage is called the Hall effect.

Hall Voltage

- The transverse voltage builds up until the

electric field it produces exerts an electric

force on the moving charges that equal and

opposite to the magnetic force. - The transverse voltage produced is called the

Hall voltage.

Charge Carriers in the Hall Effect

- The Hall voltage has a different polarity for

positive and negative charge carriers. - That is, the Hall voltage can reveal the sign of

the charge carriers.

Hall Probe

- Basically the Hall probe is a small piece of

semiconductor layer.

- Four leads are connected to the midpoints of

opposite sides.

- When control current IC is flowing through the

semiconductor and magnetic field B is applied,

the resultant Hall voltage VH can be measured on

the sides of the layer.

Force between two parallel current-carrying

straight wires (1)

- Parallel wires with current flowing in the same

direction, attract each other. - Parallel wires with current flowing in the

opposite direction, repel each other.

Force between two parallel current-carrying

straight wires (2)

- Note that the force exerted on I2 by I1 is equal

but opposite to the force exerted on I1 by I2.

Definition of the ampere

- The ampere is the constant current which, if

maintained in two parallel conductors of infinite

length, of negligible cross-section, and placed

one metre apart in a vacuum, would produce

between these conductors force of 2 x 10-7 N per

metre of length.

Torque on Current Loop

- A loop of wire carrying a current experiences a

torque. - This torque can cause it to rotate up to 1800
- ? NBAI

Moving Coil Galvanometer

- A galvanometer that is operated by the force

exerted by an electric current flowing in a

movable coil suspended in a magnetic field.

Construction of a Moving Coil Galvanometer

Linear scale

pointer

Concave pole piece

Moving coil

Soft iron cylinder

Hair spring

Moving Coil (1)

- A coil, with current I flowing through it, placed

in a magnetic field, can experience a torque ?. - ? NBAI

Moving Coil (2)

- The moving coil is hung from a spring which winds

up as the coil rotates this winding up produces

a restoring torque ? proportional to the winding

up (or twisting) of the spring, i.e. to the

angular deflection of the coil ?. - ? c?
- The coil comes to equilibrium when ? ?

Radial Field

- In order to have a meter with a linear scale, the

angle between the coil and the field must remain

constant. - The angle can remain constant (90) if we have a

radial magnetic field. - The soft iron cylinder gives us this field shape.

Current Sensitivity (1)

- The current sensitivity is defined as the

deflection per unit current.

Unit rad/A or mm/?A

Current Sensitivity (2)

- The current sensitivity can be increased by
- Increasing the number of turn of coils
- but the armature will be too bulky and the size

of the air gap cannot be too small. - Increasing the magnetic field in the air gap

stronger magnet is used and the air gap should

be as narrow as possible. - Increasing the area of the coil
- but the coils will swing about its deflected

position. - Using weaker hairspring,
- but if the opposition of the suspension is too

weak the coil will also swing about its deflected

position. (reading again take time).

Voltage sensitivity

- The voltage sensitivity is defined as the

deflection per unit voltage.

Unit mm/?A

d.c. Motor

http//www.metacafe.com/watch/971400/unexplained_p

henomenon_simplest_electric_motor/

http//www.physclips.unsw.edu.au/jw/electricmotors

.html

Velocity selector for charged particles

- The speed can be obtained from the equation
- q v B q E, or v E / B

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