Electromagnetism
The Foundation Course on Physics
Professor Vojtěch Mornstein
Glencoe pp. approx. 650-709
Electromagnetism
• In this lecture, some basic laws about interactions of
magnetic fields and current-carrying conductors will be
revisited and some newly introduced.
• Good understanding of electromagnetic phenomena is not
easy. Electromagnetic field is not visible and has two
interconnected components that differ considerably in their
properties and also effects: electric and magnetic.
• Electromagnetism is the background of many devices used
in medicine and problems addressed also in medical
physics/biophysics. Some examples will be introduced.
• General advice: Do not hesitate to ask your teachers if you
have a problem: vmornst@med.muni.cz,
vbernard@med.muni.cz, and in close future
danvlk@med.muni.cz
Magnetic fields
Magnetic fields can be produced by
1) permanent magnets and
2) by moving electric charge, i.e. by electric
current, oscillations of charges etc.!
Magnetic field produced around a
straight wire carrying a current
Each moving electron produces an anti-clockwise magnetic field (B) around itself when
viewed along the direction of its motion. However, in the picture below we follow not
the electrons but the current!!! Direction of the electric current is opposite.
Magnetic flux density B around an infinite straight conductor (a wire) in vacuum can be
calculated according the formula:
[T]
where I [A] is the electric current, d [m] is the distance of a measurement point from the
wire. See also Fig. to determine the orientation of the vector B. „Right hand rule“ –
thumb has the same direction as current, curled fingers show the direction of B.
Note: The current is represented by flow of positive charges (based on historical issues of
physics). The electrons move in opposite direction.
d
I
B


2
0
=
Magnetic field resulting from a coil
carrying a current
A coil or solenoid carrying a current produces magnetic field and
behaves similarly to a permanent magnet, N and S poles can be
distinguished in them as well.
The following formulas can be derived using complex theory of magnetism. In
this theory vector calculus is used in which are defined the directions of
vector products. That is why we must use various left- and right-hand rules to
find directions of the respective vectors instead of correct mathematics.
2. Magnetic flux density in the middle of a circular coil (a simple wire
loop):
[T],
where I [A] is the electric current, r [m] is the radius of the coil.
r
I
B
2
0
=
N
S
Multi-layer coil
r
IN
B
2
0
=
http://info.ee.surrey.ac.uk/Workshop/advice/
coils/air_coils.html
N – number of turns,
b and c should be very
small in comparison with
the radius of the coil. B is
valid again for the middle
of the coil.
Magnetic field resulting from an infinite
solenoid carrying a current
• 3. Magnetic flux density B inside an infinite solenoid (a long helical coil):
B = 0nI [T] (vacuum or air within the solenoid) and
B = nI [T] (valid for a solenoid with a core of material having  = r0),
I [A] is the electric current and n the number of solenoid turns per meter (i.e.
n = N/L, where N is the total number of turns and L is the length of the
solenoid).
Note: there is no dependence on radius! The field inside the infinite (very
long, say) solenoid is homogeneous.
Another „right hand rule“ –
the thumb points to the N
pole of the solenoid =
electromagnet
In Medicine: MRI
(Magnetic Resonance Imaging)
The patient is placed in a strong magnetic field produced by a powerful
electromagnet. B = 1 to 3 T!
Enroll in medical faculty – you will get to know more!
http://www.biomedresearc
hes.com/root/pages/resear
ches/epilepsy/mri.html
Magnetic force on a conductor carrying
current
If a straight wire carrying current I is positioned in a homogeneous magnetic field making
an angle a with the vector of magnetic flux density B (see Fig. b), the force acting on it can
be calculated:
F = BLlsina [N],
where L is the length of the wire exposed to the magnetic field.
Thus, a magnetic flux density 1 T exists if the force exerted on a straight wire of 1 m length
is 1 N when the wire carries a current of 1 A and is placed at right-angles to the direction of
the magnetic flux B.
To determine the direction of the force exerted: Align one of the externally applied
magnetic lines to be parallel with and touching one of the magnetic lines produced by the
current. The direction from this common point to the conductor gives the direction of force
on the conductor. See Fig. c!!!!
Magnetic force on a conductor
carrying current
Or: Fleming's Left Hand Rule – compare both methods
Magnetic force between two parallel
conductors
The force per unit length on wire „B“ (carrying current IB) due to the
magnetic field produced by the current IA in the wire „A“ is given by:
[N],
where d is the perpendicular distance between the wires. If the currents
have the same direction the wires are attracted. In case they have opposite
direction they are repelled. Imagine also a beam of charged particles – what
can happen?
Definition of 1 ampere in SI is based on the above formula:
A current of 1 A flows in one infinite straight wire if an equal current in a
similar wire placed in parallel 1 meter away in a vacuum produces a mutual
force of 0/2 N per 1 meter of length (i.e. 2·10-7 N·m-1, since
0 = 4·10-7 N·m-1).
d
II
F BA


2
0
=
Magnetic deflection of a moving
electron/charged particle
The force on an electron (or other particle) with charge e travelling at velocity v
at an angle Θ (capital theta) between the velocity and a magnetic flux density B
is given by:
F = BevsinΘ [N].
To determine the direction of this force we can use the same rule like for the
force exerted on a wire carrying electric current because the moving electron
represents also an electric current (flowing in opposite direction compared
with conventional direction of current).
Deflection of moving electrons/charged particles by magnetic field is exploited
e.g. in electron microscopes, mass spectrometers (see Glencoe pp. 706-707)
and some accelerators.
Electromagnetic
induction
Voltage induced in a straight wire
Voltage induced across two ends of a straight wire moving in magnetic field B is given by:
V = BLvsina [V],
where L is the length of the conductor (wire) [m], v is the velocity of the conductor [m.s-1],
and a is the angle between v and the wire. We assume that the vector v and the wire are
perpendicular to B. If not, we have to calculate with their components lying in the plane
perpendicular to B (B is the plane of this page). See also Fig. : A wire moving in magnetic
field. L is the length of the wire (a conductor), v is its velocity.
Electromagnetic induction
Voltage induced in a solenoid
In general, electromagnetic induction is the production of
an electric voltage (and hence a current) in conductors
due to a changing magnetic field. It is described by the
Faraday’s laws:
A change of the magnetic flux linked with a conductor
induces an electromotive force (voltage) in the conductor.
The magnitude of the induced electromotive force is
proportional to the rate of change of magnetic flux
linkage
The “linkage” is the
number of force lines intersected by the moving conductor
or
the product of the change of magnetic flux D and number
of turns in a solenoid N. (For a single wire loop N = 1!)
Electromagnetic
induction
For the induced voltage V we have:
[V],
where DN is the change of magnetic flux linkage, Dt the
time of change, and N the number of turns in a
solenoid.
Lenz’s law: The direction of the induced current in a
conductor caused by a changing magnetic flux is such
that its own magnetic field opposes the change in
magnetic flux. (That is why there is the „-“ sign in the
above formula.)
t
N
V
D
D
−=
Self-inductance
A change of current through a coil induces a voltage which acts against the
current change. Voltage appears both at increase or decrease of the current.
Voltage induced by change of current in a solenoid:
It is given by the formula:
[V]
where L* is the self-inductance of the solenoid and
[H – henry]
In the last formula, N is the number of solenoid turns, l is the length of the
solenoid [m], A is the cross-sectional area of the solenoid [m2], and  is the
permeability of the medium inside the solenoid.
t
I
LV
D
D
=
*not length of a wire!!!!
l
AN
L
2
=
Self-inductance
Sudden interruption of a current flow through a solenoid
produces a high voltage impulse that demonstrates as
a spark!
This is also the principle
of ignition coil that is
connected to spark
plugs in a car
combustion motor.
Gasoline aerosol is
ignited by the electric
sparks.
Electromagnetic induction: where to
find it in practice? Everywhere!
Few examples:
Wireless transfer of electric energy – even into implants
inside the body
Induction heating plates
Induction heating of tissues – diathermy
Production of electricity (alternating current)
Melting metals
Transformers (next lecture)
………………………. Etc. , etc., etc.
Safe recharging of an electric toothbrush or
wireless chargers for smartphones!!!!
Wireless transfer of electric energy –
even into implants inside the body
Induction heating plates
20 kHz
This magnetic field
looks rather bizarre!
It doesn´t matter☺.
Iron pots are heated,
nothing else!
diathermy
Compact coil
applicator
Eddy currents
Production of electricity
Melting metals by
induction
platinum
gold
titanium
Electric toothbrush charging
Battery can be charged
Wireless Chargers for Smartphones
Battery can be charged
Electric joke
February 2020