Magnetic Fields
Magnetic fields emerge from the North pole
of a magnet and go into the South pole. The
direction of the field lines show the direction
of the force that a ‘free’ North pole would
experience at that point.
Magnetic fields are created by moving charges. In the case of a wire,
these charges are free electrons. In a permanent magnet, the
movement of electrons within atoms creates tiny currents, which set
up a magnetic field .
The right hand grip rule gives the direction of
the field lines around a long current carrying wire.
Imagine you are gripping the wire, with your thumb
pointing in the direction of the current. Your
fingers then show the direction of the field lines.
An electromagnet makes use of the magnetic field
created by a current. One end becomes a North
pole, where the field lines emerge from, and one
end becomes a South pole. To identify the poles,
look at it end on and decide which way the
current is flowing:
Current anticlockwise
= North pole
Current clockwise =
South pole
Magnetic force
A current carrying wire is surrounded
by a magnetic field. The magnetic field
of the current carrying wire can
interact with the external magnetic
field of the permanent magnet. The
wire will move, showing that a force is
acting on it.
Fleming’s left
Hand Motor Rule
predicts the direction
of the force on the
current carrying
conductor. The motion,
field and current are
mutually perpendicular.
The ‘strength’ of a magnetic
field is magnetic flux
density, B. This can be
imagined as the number of
field lines passing through
a region per unit area. The
magnetic flux density is
greatest when closest to the
poles of the bar magnet. It
gets smaller as you move
further away.
Magnetic flux density is measured in
tesla. The tesla can be defined:
To define magnetic flux
density:
𝑭
𝑩=
𝑰𝑳
F = force (N)
B = magnetic flux density (T)
I = current (A)
L = length of conductor
perpendicular to field (m)
Mutually perpendicular
The magnetic flux density is one tesla when a wire
carrying current of 1A placed at right angles to
the magnetic field experiences a force of 1N per
metre of its length.
So, the size of the force on a current carrying wire
perpendicular to a magnetic field is proportional to the
current, the length of wire and the magnetic flux density :
F= BIL. If however the wire is at an angle other than 90°:
F = BIL sinθ
The force is
greatest when
the wire and the
field are
perpendicular to
each other
(because sin 90 is
1, so this is where
the component of
the magnetic field
perpendicular to
the current is the
greatest)
where θ is the angle between the magnetic field and the
current or conductor.
The force is 0 when the magnetic field and the
current are parallel (because sin 0 is 0)
Magnetic Forces on Moving Charges
𝑭 = 𝑩𝑸𝒗
The force on a moving charge is determined by the
magnetic flux density, B, the charge, Q, and the
velocity of the particle, v.
The force F is always at right angles to the particle’s velocity, v, and its direction can be found using
Fleming’s left hand rule.
For a charged particle moving in a circle, the BQv
force acts as a centripetal force. We can use
this to calculate the radius of an orbit of a
charged particle in a magnetic field:
𝑚𝑣 2
𝑟
= 𝐵𝑄𝑣
hence
𝑚𝑣
=𝑟
𝐵𝑄
This equation shows that:
 Faster moving particles move in bigger circles – velocity is directly proportional to radius
 Particles with a larger mass move in bigger circles – mass is directly proportional to radius
 A stronger field will cause particles to move in a smaller, tighter circle – magnetic flux
density is inversely proportional to radius.
A deflection tube is designed
to show a beam of electrons
passing through a combination
of electric and magnetic
fields. By adjusting the
strength of these fields, you
can balance the forces on the
electrons so that the beam
remains horizontal.
An electron had charge –e, and an
amount of work QV is done when
accelerating it from cathode to
anode. This work is equal to its
kinetic energy. We therefore have:
𝟏
eV = m𝒗𝟐
𝟐
If the electron beam remains straight,
the electric force must be equal to the
magnetic force:
EQ = BQv
E = Bv
𝑬
𝒗=
𝑩
Mass Spectrometers
A mass spectrometer allow
the masses of ions to be
found with greater accuracy
– enough to determine the
empirical formula – as well as
the relative abundances of
each ion.
A mass spectrometer gives molecules a
positive charge of +e in the ion source,
where they are then accelerated through a
voltage V.
They then pass through a strong magnetic
field.
The speed of the particles can be
determined by the ‘velocity selector’. The
velocity of a particle v is E/B, so by changing
the magnetic field strength and electric field
strength, particles of a particular velocity
can be chosen.
The ions of heavier molecules are deflected
less than lighter ones – the radius gets
larger as m gets larger.
Only ions travelling at a particular radius can
pass through the slit and into the detector.
The detector is connected to a computer
which identifies the ions from their mass to
charge ratio and records the amount of each
ion.