Hans Christian Oersted discovered in 1819 that a compass needle is deflected by a current-carrying wire, demonstrating the relationship between electricity and magnetism. A current produces a circular magnetic field around it, and the direction of the magnetic field can be determined using the Right-Hand Grip rule. Maxwell's equations relate electric and magnetic fields and show that changing magnetic fields produce electric fields and vice versa. Magnetic fields exert forces on moving charges and electric currents. These forces allow applications like electromagnets, electric motors, and particle accelerators.

1. Electricity and Magnetism

2. Magnetic Effect of a Current
In 1819, Hans Christian Oersted
accidentally discovered that a
compass needle deflected when
the current was switched on.

3. Oersted’s Experiment

4. A current-carrying conductor produces a
magnetic field around it

5. • Magnetic field pattern around
a straight wire.
• The resulting magnetic field
lines form concentric circles
around the wire.
The Right-Hand Grip rule can
be used to predict the
direction of the magnetic field

6. Magnetic field around a wire carrying current
The magnetic field of a long, straight current-
carrying wire is stronger:
1) when it is closer to the wire, or
2) when a larger current flows through the wire.

7. Maxwell’s Equations
Relate Electric and Magnetic fields generated by
charge and current distributions.
1,,In vacuum 2
0000 cHBED

t
D
jH
t
B
E
B
D






0
E = electric field
D = electric displacement
H = magnetic field
B = magnetic flux density
= charge density
j = current density
0 (permeability of free space) =
4 10-7

8. Maxwell’s 1st Equation
000
1 Q
dVSdEdVEE
VSV

0
2
0
3
0
4
4
q
r
dSq
SdE
r
r
q
E
spheresphere


0
E

8
Equivalent to Gauss’ Flux Theorem:
The flux of electric field out of a closed region is proportional to
the total electric charge Q enclosed within the surface.
A point charge q generates an electric field
Area integral gives a measure of the net charge
enclosed; divergence of the electric field gives the density
of the sources.

9. Gauss’ law for magnetism:
The net magnetic flux out of any
closed surface is zero. Surround
a magnetic dipole with a closed
surface. The magnetic flux
directed inward towards the
south pole will equal the flux
outward from the north pole.
If there were a magnetic
monopole source, this would
Maxwell’s 2nd Equation0B

00 SdBB

Gauss’ law for magnetism is then a
statement that There are no magnetic
monopoles

10. Equivalent to Faraday’s Law of Induction:
(for a fixed circuit C)
The electromotive force round a
circuit is proportional to the rate of
change of flux of magnetic
field, through the circuit.
Maxwell’s 3rd Equation
t
B
E


dt
d
SdB
dt
d
ldE
Sd
t
B
SdE
C S
SS




ldE

SdB

N S
Faraday’s Law is the basis for electric
generators. It also forms the basis for
inductors and transformers.

11. Maxwell’s 4th Equation
jB

0
t
E
c
jB


20
1
ISdjSdBldB
C S S
00

Originates from Ampère’s (Circuital) Law :
Satisfied by the field for a steady line current (Biot-
Savart Law, 1820):
r
I
B
r
rldI
B
2
4
0
3
0
currentlinestraightaFor


Ampère
Biot

12. Magnetic field pattern around a flat coil
The magnetic field of a straight wire
wound into a flat coil.
The magnetic field at the centre of
the coil is stronger as the magnetic
field lines are closer.
There are two ways to increase the
magnetic field strength at the centre
of the flat coil:
1) Increase the current.
2) Increase the number of turns of
the coil.

13. For loop or coil of wire, can
still use 1st RHR, but direction
of current constantly changes.
Easier to use 2nd Right Hand
Rule. Fingers curl in direction
of current, thumb points to
direction of magnetic field.

14. Magnetic field of a loop of wire
carrying current
R
I
B o
2

15. Magnetic Field of Multiple Stacked
Loops of Current-Carrying Wire
• The strength of the field is greater than in a single loop.
R
IN
B o
2
N is the NUMBER of loops

16. Magnetic Field of a Solenoid
nIB centersolenoid 0,
A solenoid is a helix, so it behaves
differently than stacked loops. The major
factor for the magnetic field produced by
a solenoid is the turn spacing.
n is the turn density, the number of turns
per unit length (n = N/L)
At the ends of the solenoid, about half the
field “leaks out”.
nIB endssolenoid 02
1
,

17. Magnetic Force
• If current exert forces on magnets, then
magnets ought to exert forces on currents.
• Ampere:
– passed current through two parallel wires
– one fixed wire and one suspended to swing freely
– free wire swung in response to B-field produced
by current passing through other wire

18. Force on a Moving Charge• A charge q moving through a magnetic field (B) with
velocity v, experiences a force, FM, proportional to q, v,
and B.
• Only relative motion is necessary. Charge can be at rest
and the magnetic field can be moving relative to the
charge.
• Direction of the magnetic force is perpendicular to the
plane determined by the velocity and B-field vectors.
• Magnitude of FM depends on angle between v & B.
• When particle moves parallel to the field, the force is zero.
When the particle moves perpendicular to the field, the
force is a maximum.
sinqvBFM

19. Force on a Moving Charge

20. 3rd Right Hand Rule Version A
• Gives direction of the magnetic force exerted on a conventional
current (or positive charge) by an external magnetic field
• Point fingers of RH in direction of current (or motion of charge)
• Curl fingers through smallest angle to direction of magnetic field
• Thumb indicates direction of the force.
• If charge or current is negative, direction of force is opposite
(or use left hand).

21. 3rd Right Hand Rule Version B
• Point thumb of RH
in direction of
current (or motion
of charge)
• Straight fingers
point in direction of
magnetic field
• Palm pushing
indicates direction
of magnetic force

22. Magnetic Deflecting Force on
a Charged Particle
• Because FM is perpendicular
to v, it is a deflecting force.
• It changes the direction of v,
without changing the
magnitude.
• No work is done on a moving
charge by a B-field.
• No change in the particle’s
energy will occur in the
process.

23. Magnetic Deflecting Force on
a Charged Particle
• If the field is large enough, the direction of the force on the particle will
continuously change, but will always be perpendicular to the charge’s
velocity.
• The particle will be forced to move in a circular arc (or even a complete
circle).

24. Particles in a Magnetic Field: What is
the direction of the particle velocity?

25. Trajectory of a Free Particle
• The particle
experiences a
centripetal acceleration.
• The magnetic deflecting
force is therefore a
centripetal force.
• If v is perpendicular to
B, the radius of the
charged particle’s
trajectory can be easily
predicted. qB
mv
R
R
mv
qvB
R
mv
Fcent
2
2
momentum

26. Particle Accelerators• In a particle accelerator, the goal is to obtain the largest possible
momentum, mv.
• This is done by imparting energy to the particle, such as by applying
an external E-field. This will increase the momentum of the particle.
• Simultaneously increasing
the B-field will keep the
radius constant.
• In a particle accelerator, the
largest possible field and
radius are required for a
given charge.
• At Fermilab and CERN, the
particle accelerators are 6.3
km and 27 km in
circumference, respectively.

27. Television Screens
• Consists of cathode ray tube
(CRT) in which electric fields
form a beam of electrons.
• Phosphor on the TV screen
glows when struck by beam.
• Pair of coils on the tube neck
create a set of perpendicular
magnetic fields.
• As the electron beam passes
through each set of coils, it is
deflected either horizontally or
vertically to different regions
of the screen.
• The current through the coils
can be varied, thereby
varying the magnetic field and
the degree of deflection.

28. Particles in Magnetic Fields
• All freely accelerating charges radiate
electromagnetic energy (we will discuss
this in depth later in the year).
• Therefore, a charged particle moving
through a magnetic field will lose energy
as it experiences a centripetal
acceleration.
• If it loses kinetic energy, the radius of its
trajectory will decrease and it will spiral
inward.

29. Forces on Wires
• Consider a quantity of
charge q passing
through a wire in a B-
field, such that in time
t, the charges travels a
length of wire l.
• Direction of the force is
the same as the
direction of the force on
the individual positive
charge carriers. Use
RHR. sin
sin
sin
sin
IlBF
BtvtqF
t
t
qvBF
qvBF
tvl
tqI
M
M
M
M

30. Magnetic Force on Current-
Carrying Wire

31. Force on a Current Loop• Imagine a lightweight current-carrying rectangular coil placed in uniform
B-field.
• Direction and magnitude of the force on each segment of wire depends
on the wire’s orientation in the B-field.
• Forces may or may not cause the loop to rotate.
No rotation
when loop is
perpendicular
to B-field.

32. Torque on a Current Loop
• Suspend the loop so it can rotate freely about a
vertical axis and place it in a uniform horizontal B-
field.
• If the loop is not perpendicular to the field, the
forces on the vertical segments of wire produce a
torque that rotates the coil through the field.
• The torque on the current loop is given by
where is the angle between the magnetic dipole
moment and B.
sinNIAB
The DC motor is simple, yet very important application.

33. Magnetic Dipole Moment• Tendency of a magnet to
align with external B-field.
• For a planar loop, direction
is given by Right-Hand-
Current Rule (2nd RHR)
• Magnitude is product of
current in the loop and area
of the loop.
• Analyzing the torque on the
current loop, it is clear why
the magnetic moment tends
to align with the external B-
field.
IAl

34. Two Parallel Wires
• Two long parallel wires suspended next to each other
will either attract or repel depending on the direction of
the current in each wire.
• B-field produced by
each wire interacts
with current in the
other wire
• Produces magnetic
deflecting force on
other wire.
• Wires exert equal
and opposite forces
on each other.

35. Two Parallel Wires
Currents in Same Direction…
Wires Attract
Currents in Opposite Directions…
Wires Repel

36. Two Parallel Wires
• B-field produced by wire 2 at the position
of wire 1 is given by
where d is the distance between the wires.
d
I
B
2
20
2

37. Two Parallel Wires
• Since the wires are
parallel, the force
exerted by wire 2 on
wire 1 is given by
• However, it is often
more appropriate to
determine the force
per unit length on the
wire.
d
II
lF
d
I
lIF
lBIF
M
M
M
2
2
210
20
1
21
d
II
BI
l
FM
2
210
21

38. Magnetic field pattern around a flat coil
A solenoid is obtained by increasing the number
of turns of a flat coil.
The resulting magnetic field pattern of a
solenoid resembles that of a bar magnet.

39. Magnetic field pattern around a flat coil
The magnetic field strength in a
solenoid can be increased by:
1) increasing the current,
2) increasing the number of turns
per unit length of the solenoid, or
3) placing a soft iron core within the
solenoid. The soft iron core
concentrates the magnetic field
lines, thereby increasing the
magnetic field strength.

40. Uses of Electromagnets
1) Circuit Breaker - A safety device that switches off the
electric supply when excessive current flows through the
circuit. Uses an electromagnet to open the circuit.
Normal condition
The basic circuit breaker consists of a
simple switch, connected to either a
bimetallic strip or an electromagnet. The
diagram on the left shows a typical
electromagnet design.
The hot wire in the circuit connects to
the two ends of the switch. When the
switch is flipped to the on position,
electricity can flow from the bottom
terminal, through the electromagnet, up
to the moving contact, across to the
stationary contact and out to the upper
terminal.

41. Circuit breaker in operation
The electricity magnetizes the electromagnet.
Increasing current boosts the electromagnet's
magnetic force, and decreasing current lowers
the magnetism. When the current jumps to
unsafe levels, the electromagnet is strong
enough to pull down a metal lever connected
to the switch linkage. The entire linkage shifts,
tilting the moving contact away from the
stationary contact to break the circuit. The
electricity shuts off.

42. Uses of Electromagnets
2) Magnetic Relay - A device to control the switch of
another circuit without any direct electrical contact
between them.

43. Uses of Electromagnets
3) Electric Bell - The electromagnet
forms the core of the electric bell.
When the bell button is pressed, the
circuit is closed and current flows.
The electromagnet becomes
magnetised, attracting the soft iron
armature and the hammer strikes the
gong. However, the circuit will
break and the electromagnet loses its
magnetism and the springy metal
strip pull back the armature and the
circuit is closed again. The process
repeats.

44. Uses of Electromagnets
4) Magnetic Resonance Imaging
(MRI) - A popular method of
medical imaging that provides
views of tissues in the body. It is a
huge scanner containing a solenoid
made of superconductors.

45. Force on current-carrying conductors
- When you placed a current-carrying wire in a magnetic
field, the wire experiences a force. This is called the
motor effect.
- This force acts perpendicular to both the direction of the
current and the direction of the magnetic field.

46. Force on current-carrying conductors
A change in the direction of the current in the wire will
cause a change in the direction of the force, with the
direction of the magnetic field staying constant.
Similarly, a change in the direction of the magnetic field
will cause a change in the direction of the force, with the
direction of the current in the wire staying constant.

47. Force on charge particles
- When you placed a charged
particle in a magnetic field, it
experiences a force.
The direction of deflection for
these charged particles can be
predicted by Fleming’s left hand
rule.

48. Force on charge particles
Magnetic field into page
Positively charged particle deflected
upwards
Negatively charged particle
deflected downwards
A change in the direction of the magnetic field will cause a
change in the deflection of the charged particles, with the
direction of the particles staying constant.

49. Fleming’s Left-Hand Rule
We can easily deduce the direction of the force on the
current-carrying wire when it is placed in a magnetic field
using Fleming’s Left-Hand Rule. It helps us to predict the
direction of motion or force.

50. Why does a current-carrying conductor experience a
force when placed in a magnetic field
-Magnetic fields that are in the same direction make the
combined fields stronger.
-Magnetic fields that are in opposite direction make the
combined fields weaker.

51. The force between two parallel wires
If we place two current carrying wires held parallel to each other, they
always attract or repel each other. The direction of force of attraction is
given by the Fleming’s left hand rule. According to the Fleming’s left
hand rule, if we stretch our fore finger , middle finger and the thumb of
left hand so that they are mutually perpendicular to each other, then the
fore finger indicates the direction of produced magnetic field due to the
another wire, middle finger indicated the direction of current in the wire
and the thumb indicates the direction of force.

52. The force between two parallel wires
Parallel wires carrying currents will exert forces on each other. One wire
sets up a magnetic field that influences the other wire, and vice versa.
When the current goes the same way in the two wires, the force is
attractive. You should be able to confirm this by looking at the magnetic
field set up by one current at the location of the other wire, and by
applying the right-hand rule.

53. The force between two parallel wires
Parallel wires carrying currents will exert forces on each other. One wire
sets up a magnetic field that influences the other wire, and vice versa.
When the currents go opposite ways, the force is repulsive. You should
be able to confirm this by looking at the magnetic field set up by one
current at the location of the other wire, and by applying the right-hand
rule.

54. Force on a current-carrying rectangular coil in a
magnetic field
The catapult effect shows the force on a wire in a
magnetic field when current flows through the
wire.
It follows then that a wire in a field from a
permanent magnet will feel a force when current
flows through it. The magnetic field generated
around the wire by the current will interact with
the field around the magnet and the two fields
will push or pull on each other.
The magnetic field around a straight wire is
circular. The magnetic field between two
attracting poles is straight. When the two
interact, the wire is pushed away from the field
between the attracting poles at right angles (90°)
both to the straight field lines and to the direction
of current flow.

55. The D.C. Motor
A direct current (DC) motor is a fairly simple electric motor that uses
electricity and a magnetic field to produce torque, which turns the
motor.

56. The D.C. Motor
A split - ring commutator (sometimes just called a commutator) is a simple and
clever device for reversing the current direction through an armature every half
turn. The commutator is made from two round pieces of copper (held apart and
do not touch each other), one on each side of the spindle. A piece of carbon
(graphite) is lightly pushed against the copper to conduct the electricity to the
armature. The carbon brushes against the copper when the commutator spins.
As the motor rotates, first one piece of copper, then the next connects with the
brush every half turn.The wire on the left side of the armature always has
current flowing in the same direction, and so the armature will keep turning in
the same direction.

57. Current in this arm flowing from left to
right.
Current in the same arm reverses,
flowing from right to left.
Current stops flowing momentarily in
the coil but inertia will propel it to make
contact once again, reversing the
current in the coil.

58. To increase the turning effect on the wire coil, we can:
1) increase the number of turns on the wire coil.
2) increase the current in the coil.
3) Insert a soft-iron cylinder at the center of the coil of wires.

59. A.C. motor
An AC motor is an electric motor that is driven by an alternating
current. It consists of two basic parts, an outside stationary stator having
coils supplied with alternating current to produce a rotating magnetic
field, and an inside rotor attached to the output shaft that is given a
torque by the rotating field.

60. Similarities & Differences between A.C. / D.C. Motor
DC Motor AC Motor
Similarities 1. To convert electrical energy
to rotational mechanical energy.
1. To convert electrical power to
rotational mechanical energy.
Differences 1. Commutator present.
2. Cheap.
3. Fixed speed.
4. Requires direct current.
1. Absence of commutator
(use slip rings).
2. Expensive.
3. Variable speed.
4. Requires alternating
current.