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 Earth’s 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 lesseron this side of the wire

Net flux is greateron this side of the wire

I

Fleming’s 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.

BIF

sinBIF

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.

IF

B

Unit : tesla (T) or gauss (G), 1 G = 10-4 T or weber/m2

Typical Values of the magnetic flux density

Source B-Field (Tesla)

Human Brain 10-12

Interstellar Space 10-10

Near Household Wiring 10-4

Sunlight 3x10-5

Earth's Magnetic Field at Pole 5x10-4

Sunspots 0.3

Largest man-made Magnet 5.0

Surface of a Nucleus 106

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

IB

rP •TThis relationship is valid as long as r, the p

erpendicular distance to the wire, is much less than the distance to the ends of the wire.

Calculation of B near a wire

r

IB o

2

)m (H A m T 104 -1-17 o

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

IB N

B and

So we have

NI

B o

or nIB o

where N

n

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, nB o2

1'

B

Distance from the centre of the solenoid0

nIB o

nB o2

1'

212

1

Magnetic Flux Density due to Some Current-carrying conductors(1)

• Circular coilr

NIB o

2

• Helmholtz coilsr

NI

r

NIB oo

72.0125

8

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/bu_semester2/c12_force.html

sinqvBF

BvqvBF for max

BvF //for 0

Right Hand Rule

• Direction of force on a positive charge given by the right hand rule.

BvqF

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.

qvBqE

r

mvqvB

2

'

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/auroras/selfguide1.html

Hall Effect• 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.

• 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.

• Four leads are connected to the midpoints of opposite sides.

Force between two parallel current-carrying straight wires (1)

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

2. 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.

a

IIF o

221

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.