wu4c10 by adel khamis
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Unit Four -438- Chapter Ten
Magnetic Effect of an Electric Current
Christian Oersted:
In 1819, Oersted discovers that the electric current produce magnetic field.
The Magnetic flux intensity (B):
Magnetic field consists of lines called ………………………………
The total number of flux lines () has unit of …………
Magnetic flux density (B) is: …………………………………………….
Rule: ………………………
Its unit is …………………………. or ……………..……………….
Magnetic field due to a current in a straight wire:
Magnitude:
The relation between magnetic field intensity and the electric current intensity
is …………….…….
B ………
The relation between magnetic
field intensity and the distance is
…………….…….
B ………
Where:
: The permeability of the medium, and its value for air or space equals
4 x10-7 and its unit is ………………. or ………………….
I: means ………………………….
Work Sheet 2008/2009
Unit Four -439- Chapter Ten
d: means ……………………………………………………………….
Shape:
It is …………………………………………………………………..
The circular magnetic flux lines are ………. near the wire, and
…………. as the distance from the wire increases.
Direction:
It can be indicated by using of three methods:
a) Ampere’s right hand rule:
……………………………………………………
……………………………………………………
……………………………………………………
……………………………………………………
b) Using a small compass:
……………………………………………………
……………………………………………………
……………………………………………………
c) Right hand screw rule:
……………………………………………………
……………………………………………………
……………………………………………………
……………………………………………………
Work Sheet 2008/2009
Unit Four -440- Chapter Ten
Neutral point:
Defination: …………………………………………………………………..
In case of two wires carrying current in the same direction the newtral point
will be (between them/ outside the wires)
In case of two wires carrying current in opposite direction the newtral point
will be (between them/ outside the wires)
Neutral point form close to the wire that carry (low, high) current.
Example:
1. Determine the magnetic flux density at a distance of 10 cm in air from the
center of a long wire carrying a current of 10 A. = 4 x 10-7 wb/A.m
…………………………………………………………………………………
…………………………………………………………………………………
…………………………………………………………………………………
…………………………………………………………………………………
[2 x 10-5 tesla]
2. Two straight line wires, the first carry 2A and the second carry 8A. Find
the distance between the two wires if the neutral point between them at 4
cm apart from the first wire.
…………………………………………………………………………………
…………………………………………………………………………………
…………………………………………………………………………………
…………………………………………………………………………………
[20 cm]
Work Sheet 2008/2009
Unit Four -441- Chapter Ten
3. Two straight line wires, the first carrying 2 A and the distance between
them is 50 cm. if the neutral point was at 10 cm apart from the first wire
when the current in both of them was at the same direction find the
position of the neutral point if the current in one of them is inverted.
…………………………………………………………………………………
…………………………………………………………………………………
…………………………………………………………………………………
…………………………………………………………………………………
[16.6 cm]
Magnetic field due to current in a circular loop:
The Magnitude:
The relation
between magnetic field
intensity and the electric
current intensity is …………….…….
B ………
The relation between magnetic field intensity and the radius is …………….
…….
B ………
Where:
: …………………………………………………………………….
N: ……………………………………………………………………..
I: ……………………………………………………………………..
Work Sheet 2008/2009
Unit Four -442- Chapter Ten
r: ……………………………………………………………………..
Shape:
………………………………………………………………………………..
………………………………………………………………………………..
Direction:
………………………………………………………………………………..
………………………………………………………………………………..
………………………………………………………………………………..
Example:
1. Determine the magnetic flux density at the center of a circular loop of
radius 11 cm carrying a current 1.4 A. If the wire consists of a coil having
20 turns.
………………………………………………………………………………..
………………………………………………………………………………..
………………………………………………………………………………..
[1.6 x 10-4 tesla]
2. circular coil consists of 20 loops carrying current of 1A, find the current
that pass in a straight line wirre tangent to the coil to vanish the flux
intensity at the center of the circular coil.
………………………………………………………………………………..
………………………………………………………………………………..
………………………………………………………………………………..
[62.8A]
Work Sheet 2008/2009
Unit Four -443- Chapter Ten
Magnetic field due to current in a solenoid:
Magnitude:
The relation between magnetic field intensity and the electric current intensity is
…………….……., B ………
The relation between magnetic field intensity and the length of the solenoid is
…………….……., B ………
Where:
: …………………………………………………………………….
N: ……………………………………………………………………..
I: ……………………………………………………………………..
L: ……………………………………………………………………..
n: ……………………………………………………………………..
Work Sheet 2008/2009
Unit Four -444- Chapter Ten
Shape:
…………………………………………………………………………………
……………………………………
Direction:
…………………………………………………………………………………
…………………………………….
Examples:
1. A long solenoid has 800 turns. The current flowing through the wire is
0.7 A. Find the magnetic flux density in the interior of the solenoid. Knowing that
its length is 20 cm.
…………………………………………………………………………………
…………………………………………………………………………………
…………………………………………………………………………………
[3.52 x 10-3 Tesla]
2. A solenoid is constructed by winding 800 turns of wire on a 20 cm iron
core. What current is required to produce a flux density of 0.815 Tesla in the
center of the solenoid? The permeability of iron is 1.63 x 10-2 wb/A.m
…………………………………………………………………………………
Work Sheet 2008/2009
Unit Four -445- Chapter Ten
…………………………………………………………………………………
…………………………………………………………………………………
[1.25 x 10-2 A]
Force on a current carrying wire in a
magnetic field:
…………………………………………………………………………………
……………………………………………………………………
Direction of the motion:
The figure (A) shows the field
between the two poles of U shaped magnet.
The figure (B) shows the shaped of the
magnet field resultant from ……………………………..
When the wire is placed in the magnetic field of the magnet, the flux line
will be close to each other at the side at which ………………………….., and far
a part at a side at which …………………………………………...
Because the flux lines have ……………. force between each other, the
wire will move from the side at which …………………………. to the side at
which ……………………………………..
Direction of motion can be determined by using of Fleming’s left hand
rule:
Work Sheet 2008/2009
Unit Four -446- Chapter Ten
Fleming’s left hand rule:
…………………………………………………………………………………
…………………………………………………………………………………………
……………………………………………
Work Sheet 2008/2009
Unit Four -447- Chapter Ten
Factor affected on the magnetic motive force:
The length of the wire (L):
……………………………………………….
F ……..
The current (I):
…………………………………………………………….
F ……..
The magnetic flux density (B):
…………………………………………….
F ……..
Therefore:
F ……..
F = ……..
By using of ……….. as a unit of force, ……….. as a unit of magnetic flux
density, ………. as a unit of electric current intensity and ………. as a unit of length,
The constant is equal to one.
F = ……..
If the field is inclined by angle of to the direction of the wire
F = B I L sin
Define tesla: ……………………………………………………………..
The force between two wires carrying current in the same direction will be
(inward/ outward)
The force between two wires carrying current in opposite direction will be
(inward/ outward)
Work Sheet 2008/2009
Unit Four -448- Chapter Ten
For two wires A and B the mutual force between them can be calculated from
the relation: F = B I L sin
where:
F is ………………………………. and its unit is ……………………………….
B is ………………………………. and its unit is ……………………………….
I is ………………………………. and its unit is ……………………………….
L is ………………………………. and its unit is ……………………………….
Examples:
1. Find the unit and the dimensional formula of the magnetic flux density.
…………………………………………………………………………………
…………………………………………………………………………………
2. A wire 30 cm long supports a current of 4 amperes in a direction
perpendicular to a magnetic field. If the force on the wire is 6 Newton find the
magnetic flux density.
…………………………………………………………………………………
…………………………………………………………………………………
…………………………………………………………………………………
…………………………………………………………………………………
[5 Tesla]
3. If the wire in the previous example makes an angle of 30 with respect to
the field, find the force acting on the wire.
…………………………………………………………………………………
…………………………………………………………………………………
Work Sheet 2008/2009
Unit Four -449- Chapter Ten
…………………………………………………………………………………
[3 Newton]
4. Find the mutual force between two parallel wires; the first has length of
50 cm and carrying current of 2A while the second and length of 1 m and carrying
current of 8 A. Given that the distance between them is 20 cm and of air is
4x10-7.
…………………………………………………………………………………
…………………………………………………………………………………
…………………………………………………………………………………
…………………………………………………………………………………
[8x10-6 Newton]
Torque on a rectangular current carrying loop:
In case of rectangular current carrying loop, there is a
force per each side of the rectangular coil.
The force acts per each horizontal side will
……………. because ………………………
The double force act on the vertical sides cause a torque that can
calculated by:
= F1 d1 + F2 d2
Where:
d1 ……………………………………………………………………………..
d2 ……………………………………………………………………………..
F1 ……………………………………………………………………………..
Work Sheet 2008/2009
d
L
Unit Four -450- Chapter Ten
F2 ……………………………………………………………………………..
d ……………………………………………………………………………..
But in this case the two forces are equal in magnitude, and the center of
rotation at the center of d
= …………………………..
but F = BIL
= ………………………….
but A = L d
= …………………………
In case of N turns
= BIAN
= BIAN cos
= BIAN Sin
Where:
: is the angle between the
magnetic field and the plane of the
coil.
is the angle between the
magnetic field and the normal to plane of the coil.
The direction of circular motion is normal to the coil plane and the
magnetic field is normal to the force therefore
Work Sheet 2008/2009
Unit Four -451- Chapter Ten
the angle between the force and the direction of motion is equal to the angle
between the plane of the coil and the field.
Example:
Find the torque of coil has 200 turns and carry 0.5 A, placed in magnetic field
of 10 wb, then find the angle between the coil and the field at which the torque
decrease to half its value.
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
Electrical Measuring Instruments
Moving coil galvanometer (sensitive galvanometer):
Its operating principle is based upon:
…………………...
…………………………………………………………..
It used to measure …………………………….
It is also used to …………………………………….
Structure:
…………………………………………………..
…………………………………………………..
…………………………………………………..
…………………………………………………..
………………………………………………….
………………………………………………….
Work Sheet 2008/2009
Unit Four -452- Chapter Ten
The springs are used to:
a) …………………………………..
b) …………………………………...
c) …………………………………...
G.R.:
The permanent magnet is concave.
a) …………………………………..
b) …………………………………...
The galvanometer sensitivity:
Definition: ………………………………………………………………
It depends on …………………… and …………………….
Its unit is: ………………………………………………………………
Example:
Sensitive galvanometer has a sensitivity of 50 A per scale division. What
current is required to give full deflection of the pointer through 25 scale divisions to
the right or left of the equilibrium position?
…………………………………………………………………………………………
…………………………………………………………………………………………
[1.25x10-3A]
Direct Current Ammeter:
It based on
…………………………………………………………………………
Work Sheet 2008/2009
Unit Four -453- Chapter Ten
Ammeter is a galvanometer connected with …………. resistance in
…………….. called …………………. (R…….)
Ammeter is connected to the electric circuit in …………………...
I = …..……… + …………. (1)
V : …………. = ………… (2)
From ohm’s law:
V = ………………………. (3)
From (2) and (3):
………………. = ………………..
From (1)
Is = ………… - …………..
Benefits of the shunt:
1. …………………………………………………………………
2. …………………………………………………………………
3. …………………………………………………………………
Example:
A certain galvanometer has a resistance 2 , and a current of 5 m A is
required for full-scale deflection. What shunt resistance must be used to convert the
galvanometer to an ammeter whose maximum range is 10 amperes?
…………………………………………………………………………………………
…………………………………………………………………………………………
Work Sheet 2008/2009
G
Shunt
Ig
IS
I
Unit Four -454- Chapter Ten
…………………………………………………………………………………………
…………………………………………………………………………………………
[10-3]
In the previous problem, calculate the maximum current can be measured if
the shunt is replaced by another one of resistance 0.1 x 10-3
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
N.B.:
By decrease the shunt, I max can be measured is …………………….
I max is (directly / inversely) proportional to the shunt resistance
Sensitivity of the ammeter is (directly / inversely) propoertioinal to the shunt
resistance.
Direct current voltmeters:
It is based on
…………………………………………………………………….
Voltmeter is a galvanometer connected with ………….. Resistance in
…………… called ……………………... (R…….)
Voltmeter is connected to the electric circuit in ……………………….
Work Sheet 2008/2009
Gmultiplier
Ig
Im
Electric circuit
Unit Four -455- Chapter Ten
V = …………. + ………….. (1)
I : ……………. = …………… (2)
From (1)
Vm = ………………… (3)
From Ohm’s law:
Vm = ………………… (4)
From (3) and (4):
………………….. = ………………….
From (2):
Im = ………….
Benefits of the multiplier:
1. …………………………………………………………………
2. …………………………………………………………………
3. …………………………………………………………………
Example:
A galvanometer has an internal resistance of 0.1 and gives a full scale
deflection for a current of 1 m A. Calculate the multiplier resistance necessary to
convert this galvanometer to a voltmeter whose maximum range is 50 volts.
…………………………………………………………………………………………
…………………………………………………………………………………………
Work Sheet 2008/2009
Unit Four -456- Chapter Ten
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
[49999.9 ]
How to use the pervious voltmeter to measure 50 A.
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
…………………………………………………………………………………………
[1 ]
Questions:
Draw a graphical relation between I max and Ig of an ammeter, then mention the
slop indecation
………………………………………………………
………………………………………………………
Draw a graphical relation between V max and Ig of a voltmeter, then mention the
slop indecation
………………………………………………………
………………………………………………………
The Ohmmeter:
It is based upon: ………………..…………………
………………………………………………………..
Work Sheet 2008/2009
Unit Four -457- Chapter Ten
It consists of:
……………………………………………………………………………
…………………………………………………
The battery used has electromotive force of 1.5 volt and the micro Ameter
obtain full scale deflection at 400 micro ampere therefor, to obtain full scale
deflection of the micro ammeter, it require total resistance of …………….. .
Since the internal resistance of the microameter is 250 and the fixed
resistance is 3000 there for the variable resistance must adjust to …… to
obtain full scale deflection when no external resistance connected.
By connecting of an external resistance the pointer will point law deflation and
the external resistance can be measured.
Questions:
what is the benefit of rheostate in the ohmmeter?
……………………………………………………………………………………
……………………………………………………………………………………..
G.R.:
The scale of the ohmmeter runs backward.
…………………………………………………………………………………………
The scale is non uniform.
…………………………………………………………………………………………
Work Sheet 2008/2009
Unit Four -458- Chapter Ten
Example:
A Millie ammeter of resistance 5 its coil is capable to carry a current of 15 mA.
It is desired to use it as an ohmmeter using an electric cell of 1.5 V and internal
resistance of 1 . Calculate the required standard resistance and calculate the
external resistance when connected to it, the pointer indicates 10 mA? Calculate
the current that flows through it when connected to an external resistance of
400?
……………………………………………………………………………………
……………………………………………………………………………………
……………………………………………………………………………………
……………………………………………………………………………………
…………………………………………………..……………………………….
……………………………………………………………………………………
….
[94, 50, 0.003 A]
The following table represent the relation between the external resistance and the
current pass through the micro ammeter, draw the graphical relation between I at
y-axis and R at x-axis and from the graph find the internal resistance of the
ohmmeter and the electromotive force of its battery
Rex 0 120 300 410 500 690
I 0.01 0.008 0.00625 0.0055 0.005 0.0042
……………………………………………………………………………………
……………………………………………………………………………………
……………………………………………………………………………………
……………………………………………………………………………………
…………………………………………………..……………………………….
Work Sheet 2008/2009
Unit Four -459- Chapter Ten
……………………………………………………………………………………
….
Work Sheet 2008/2009
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