MAGNETIC EFFECT AND ELECTROMAGNETIC INDUCTION.pdf

Engineering stuffs

1. PHY 121
ELECTRICITY AND MAGNETISM
Effects of Current &
Electromagnetic Induction

2. Questions
1.) What does the direction of thumb indicate in the
right-hand thumb rule?
2.) Can two magnetic lines of force ever interact? Justify
your answer.
3.) What will happen to magnetic field due to a
circular coil carrying electric current, if the number
of turns of the coil is doubled.
4.) Why does a current carrying conductor
experiences a force when it is placed in a magnetic
field? State Fleming’s left hand rule.
5. A current of 5A is flowing through a conductor
AB. Will the current be induced in the circular wire
of given radius 1m?

3. Answers
1) Motion of the conductor.
2)No. Two magnetic lines of force never interact. If they did, it would
mean that at the point of intersection, the compass needle would point
towards two directions, which is not possible.
3) The magnetic field produced by a current-carrying wire at a given
point depends directly on the current passing through it. If the number of
turns in the circular coil is doubled, the field produced will also get
doubled
4) The current carrying conductor produce magnetic field. When this
conductor is placed in a magnetic field, it experiences a force due to
mutual interaction of these two magnetic fields.
Fleming's Left hand rule states, "When an electric current (I) flows in
a wire, and an external magnetic field (B) is applied across that flow,
the wire experiences a force (F) perpendicular both to that field and
to the direction of the current flow.“
5) Since a steady current of 5A is flowing through the conductor, no
current or emfwill be induced in the circular wire.

4. ELECTROMAGNETIC
INDUCTION
MAGNETIC EFFECT OF ELECTRIC
CURRENT

5. The force of attraction or repulsion in
and around a magnet is called
magnetism.
Magnetite or lodestone is an ore of iron
–the magnet that is found in nature.

6. When a magnet is cut into two parts

8. When a magnet is placed near a current carrying
conductor
When no current is
flowing through the circuit,
there is no deflection in
the magnetic compass.
When current flows
through the circuit, the
magnetic compass deflects.

9. Defining a magnetic field
Region around a magnet where its force can be felt is
known as the magnetic field.
Why does the iron fillings form pattern?
Due to the force exerted by the magnet, the iron filings
arrange themselves in patterns as shown above.

10. How is a magnetic field represented ?
Magnetic field is represented by
magnetic lines of forces (or) field lines.

11. What are magnetic field lines ?
It is the path taken by a unit North pole
when placed in a magnetic field.

12. Magnetic field pattern due to a bar magnet
1.The field lines start from N-
pole and enter into the S-
pole.
2.No two lines will intersect
with each other.
3.Inside the magnet the field
lines move from S-N pole.
4.The magnetic lines of
forces are crowded near
the pole.

13. If you bring iron filings or iron nails close to a
magnet, the filings or nails will get attracted to
the magnetic poles. The centreof the magnet
does not attract the filings or the nails. Why ?
Because the magnetic lines of forces are crowded
near the poles.

14. How will you find the direction of the magnetic
field of a straight conductor carrying
current?

15. To determine the direction of the magnetic field
produced in a conductor carrying current
Right Hand Thumb Rule

16. Right Hand Thumb Rule
When a current carrying conductor is held in the
right hand,
so that the thumb is stretched along the direction
of the current,
then the fingers wrapped around the conductor
gives the direction of the magnetic field.

17. What happens when the direction of the
current through the conductor is reversed?

18. Strength of the Magnetic Field
A stronger current will produce a stronger
magnetic field around the wire as shown in
Figure below.

19. S. I unit: tesla, T
Magnetic Field Intensity Units
The International System (SI) unit of field
intensity for magnetic fields is Tesla (T).
One tesla (1 T) is defined as the field
intensity generating one newton of force
per ampere of current per meter of
conductor:
T = N · A
-1
· m
-1
= kg · s
-2
· A
-1

20. Magnetic field pattern due to a circular loop
carrying current

21. (i)Increases when the
Current flowing
through the coil
increases.
(ii)Increases as the
Number of turns of
the coil increases.
(iii)decreases as the
radius of the coil
increases.
The magnetic field strength at the center of a
circular coil carrying current

22. A Solenoid
An insulated copper wire wound in the form of
a cylinder is called a solenoid.
A current carrying solenoid behaves as a bar
magnet.

23. Factors affecting the magnetic field strength
due to a current carrying solenoid
1.As the number of turns of the coil
increases, the magnetic field
strength also increases.

24. 2. As the current flowing through the solenoid
increases , the magnetic field strength also
increases.
3. As a soft iron core is introduced in a
solenoid, the magnetic field strength also
increases.
Exercise
The magnetic field inside a long straight
solenoid-carrying current is
a) Zero b) decreases as we move towards
its end c) increases (d) same at all point

25. Exercise
The magnetic field inside a long
straight solenoid-carrying current
is
a)Zero
b)decreases as we move towards
its end
c)Increases as we move towards its
end
d)Is same at all point

26. The Magnetic Field of the Earth

27. TheEarthbehaveslikeamagnetwith
thesouthmagneticpoleAofthe
magnetlocatednearthegeographic
northpoleoftheearthandthenorth
magneticpoleBnearthegeographic
southpole.
Howevernorealmagnetcouldexistin
theearth’sinteriorasitsmagnetism
wouldhavebeendestroyedbythehigh
temperatureatthemiddleoftheearth

29. Magnetic field for a long straight wire
B = µ
o l/ 2πr
µ
o –is a constant called the permeability of
free space and its value is
µ
o = 4 π ×10
-7
T.m/A
Magnetic field for a circular loops
The magnitude of the magnetic field
produced by a circular loop of N turns, at
the centreof the loop, is given by the
expression:
B = N µ
o I/ 2R ( Centre of circular loop of
radius R)

30. Magnetic field of a Solenoid
B = µ
o (N/L) I =
N/L = no of loops per length it can be
represented as n
We then have B = µ
0nI
S.I unit is tesla, T.
Exercise
Determine the magnetic field produced by the
solenoid of length 80 cm having a 360 number of
turns of the coil and the current passing through
is 15 A.

31. Solution:
N = 360
Current I = 15 A
Permeability μo = 1.26 ×10
−7
T/m
Length L = 0.8 m
The magnetic field in a solenoid formula is
given by, ….
Answer = B = 8.505 ×10
−4
T
Magnetic field inside a solenoid is nearly
uniform and aligned along the solenoid
axis.
Magnetic field outside a solenoid is small
and can be considered to be zero.

33. A current carrying conductor when placed
in a magnetic field experiences a force and
then moves.

34. Magnetic Forces

36. State Fleming’s Left Hand rule
Stretch the thumb, the fore-
finger and the centrefinger
of the left hand mutually
perpendicular to each other,
the forefinger in the
direction of magnetic field,
the centrefinger in the
direction of current, then
the
thumb will point in the
direction of the force acting
on the conductor.

37. Force on a Current-Carrying Wire
A wire of length L carrying a current I at
an angle θto a magnetic field B
experiences a force given by
F = ILB Sinθ.
Themagnitude of the magnetic force is
F = q v B sinθ
Whereqis the charge of the particle, vis
its speed,Bis the magnetic field and θis
the angle betweenvand B.

38. Practice Exercise
1.) A 52 µC charged particle moves parallel
to a long wire with a speed of 720 m/s.
The separation between the particle and
the wire is 13 cm, and the magnitude of
the force exerted on the particle is 1.4 ×
10
-7
N. Find the
(a)magnitude of the magnetic field at
location of the particle
(b) the current in the wire.

39. a) Magnetic force F = qvB
B = F/qv
Answer = 3.7 ×10
-6
T
b) Magnetic field of a wire
B = µ
o l/ 2πr
I = 2πrB/µ
o
 I = 2.4 A

40. Electromagnetic Induction
Basically,
magnetic flux is a
measure of the
number of
magnetic field
lines that cross a
given area.
that is, magnetic
field B crosses a
surface area A at
an angle.
The first step to understanding the complex nature of
electromagnetic induction is to understand the idea of
magnetic flux.
A

41. Magnetic flux Φ= BA.Wb)or Weber( Tm :Unit
cos
2
BA
AB
B
B
=
•=
For a general angle θ, the component
of the field that is perpendicular to the
loop is B COS θ; hence, the flux is Φ=
BA cos θ.
Units of magnetic flux= 1 Weber = 1 T.
m
2

42. Note that Φ= BA cos θ
Exercises
A circular antenna of area 3 m² is installed at
a place in Ikeja. The plane of the area of
antenna is inclined at 47˚with the direction of
Earth’s magnetic field. If the magnitude of
Earth’s field at that place is 40773.9 nTfind the
magnetic flux linked with the antenna.

43. Solution
B = 40773.9 nT; θ = 90˚–47˚= 43°;
A = 3m²

44. A circular loop with a 2.50cm radius is
in a constant magnetic field of 0.625
T. Find the magnetic flux through this
loop when its normal makes an angle
of @ 0°, (b) 30.0°(c) 60.0°, and (d) 90°.

45. Solution
(a) Substitute θ= 0°in Φ= BA cos θ
(0.625 T) π (0.0250 m)
2
cos 0°= 1.23 ×10
-3
T.m
2
(b) (0.625 T) π (0.0250 m)
2
cos 30°= 1.06 ×10
-3
T.m
2
c) (0.625 T) π (0.0250 m)
2
cos 60°= 6.14 ×10
-4
T.m
2
d) (0.625 T) π (0.0250 m)
2
cos 90°= 0

46. ELECTRO MAGNETIC INDUCTION
A changing magnetic field can induce a current
in a circuit. The driving force behind the
current is reffered to as the induced
electromotive force (i.e., voltage).
An induced current occurs when there is a
change in the magnetic field.
The magnitude of induced current depends on
the rate of change of the magnetic field.
Michael Faraday is generally credited with the
discovery of inductionin 1831, and James Clerk
Maxwell mathematically described it as Faraday's
law of induction.

47. Electromagnetic Induction
Electromagnetic
induction is the
scientific principle
that underlies many
modern
technologies, from
the generation of
electricity to
communications and
data storage.

48. Faraday’s law of Induction
The induced voltage (emf) is proportional
to the number of loops times the rate of
change of the magnetic field
Faraday’s law states that if the magnetic
flux in a coil of N turns changes by the
amount ΔΦin the time Δt, the induced
emf is
E = -N ΔΦ/Δt = -N Φfinal –Φinitial
 t final –t initial

49. When looking for the magnitude of the
magnetic flux and the induced current, In
such cases we use the following form of
Faraday’s law:
/E/ = N |ΔΦ| =N | Φfinal –Φinitial|
 Δt t final –t initial
The SI unit is V

50. Class Exercises
5)Aclosedcoilof40turnsandofarea200cm²,
isrotatedinamagneticfieldoffluxdensity2Wb
m־².Itrotatesfromapositionwhereitsplane
makesanangleof30ºwiththefieldtoaposition
perpendiculartothefieldinatime0.2sec.Find
themagnitudeoftheemfinducedinthecoildue
toitsrotation.
6)Abarmagnetismovedrapidlytowarda40-
turncircularcoilofwire.Asthemagnetmoves,
theaveragevalueofBcosϴovertheareaofthe
coilincreasefrom0.0125Tto0.45Tin0.250s.If
theradiusofthecoilsis3.05cm,andthe
resistanceofitswireis3.55??????,findthemagnetof
(a)theinducedemfand(b)theinducedcurrent.

51. Questions 5 and 6 Answer tips

-

52. 

53. Lenz’s Law
Lenz’s law states that an induced
current flows in the direction that
opposes the change that caused the
current.
The minus sign in Faraday’s law is
consequence of the Lenz’s Law.
Eddy Currents
These are circulating electric currents
formed in a conducting material that
experiences a changing magnetic flux.

54. Assignment
7.) A coil of 10 turns and cross sectional
area 5 cm² is at right angles to a flux
density 2 ×10‾² which is reduced to zero
in 10 s. Find the flux change and the
induced emf.
8.) The area of a 120-turn coil oriented its
plane perpendicular to a 0.20 T magnetic
field is 0.050 m². Find the average
induced emf in this coil. If the magnetic
field reverses its direction in 0.34 s.