1
Magnetism Magnetic Force Bar Magnets
Like poles repel, unlike poles attract.
Force On a Magnet in a Magnetic Field
A magnet in a uniform magnetic field experiences two equal but opposite, parallel forces, which gives it an angular acceleration, providing there is damping, it ultimately comes to rest with its axis parallel to the field. A current carrying wire also experiences a force when placed in a magnetic field. If the wire is perpendicular to the field the wire moves. There is no motion if the field is parallel to it. The force which brings about the motion of the wire is perpendicular to the plane of the conductor, and the magnetic field in which it is placed. The direction of the force is found by
Flemming’s Left
Hand Rule
.
Flemming’s Left Hand Rule
states that if the
Thumb
,
Fore Finger
and
Middle Finger
are held at right angles to each other, with the
F
ore
f
inger pointing in the direction of the
m
agnetic
f
ield, the
m
iddle
f
inger pointing in the direction of the current, then the
t
humb will point in the direction of the
m
agnetic
f
orce (or
m
ovement/
m
otion of the coil.)
Factors Affecting the Force
The effect of the current
The length of the conductor
The strength and orientation of the magnetic field (number of lines per cross section area.)
Increasing the coil current is expected to increase the field strength.
Magnetic Flux Density, B
Magnetic Field Strength is known as the flux density or magnetic field induction or B
–
field, B.
Flux density
is the force acting per unit current length on a current carrying conductor that is placed perpendicular to the direction of the magnetic field.
2 The expression for the force of a current carrying wire in a magnetic field is given by If the conductor and magnet are not p
erpendicular, but are at an angle Ɵ to each other, the
expression becomes
When Ɵ = 90
⁰
sin 90
⁰
= 1. Therefore, F = BIl. When the conductor and the field are parallel
F = 0, since sinө = 0.
A current balance is used to measure the flux density of the magnetic field. F = mg m = mass of rider
Biot
–
Savart law Flux density, B
can be found experimentally using the BiotSavart law. This law states that for a
very short length , δl of a conductor carrying a current, I, the magnitude of the ma
gnetic flux
density, B at a point P distant r from δl is Ө
is the angle between δl and the magnetic field line joining it.
The constant of proportionality is a property of the medium called the permeability of the
medium, μ.
3 The permeability of a vacu
um is μ
0
.
μ
0
= 4π X 10
7
Hm
1
μ
0
is
defined

not experimentally found.
It is logical or rational for 4π to be introduced
into the equation.
μ of air and most other materials is equivalent to μ
0
except ferromagnetic material.
Flux Density of Circular Coil
For a coil of radius r carrying a steady current, I of length δl at right angles to the field line
joining it, the f
lux density, B
is given by
Flux Density of Very Long Wire B
at a perpendicular distance, a from a very long wire carrying a current is
Flux Density of a Long Solenoid
At a point P at the end of the solenoid
4
Force On a Charge in a Magnetic Field
Since electric current is the drift of charge. It can be assumed that the force experienced by the current carrying conductor is the resultant force acting on the constituent charges. Consider a conductor of length,
l
containing
n
particles of charge Q and drift velocity v.
Force on a conductor is F = BIl sinө
If the charge moves at right angles to the magnetic field, the force on one charged particle is given by The direction of the force is given by
Flemming’s Left Hand Rule
.