wu4c11 by Adel Khamis

8/14/2019 wu4c11 by Adel Khamis

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Unit Four -251- Chapter Eleven

Electromagnetic Induction

Overview:

After Oersted discovery, where the magnetic field can be produced by the

effect of ...

Faraday discovered that electric current can be produced as a result of

.. by a conductor, and that kind of electricity is called

.

Faradays Experiments:

In the figure shown; the

galvanometer indicates

in the coil

when the magnet pushed inside the coil.

The galvanometer indicates in the coil when the

magnet pulled from the coil; but the direction of current will be

. Compared with previous case.

The galvanometer indicates if the magnet is in

case of rest even inside the coil.

Give reasons:

A galvanometer connected to solenoid deflected when a magnet bar

withdraws from the coil.

..

Conclusion:

of magnetic field close to a coil causes electromotive

force and electric current to pass through the coil.

Work Sheet 2008/2009


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Give reasons:

The E.M.F resulted in a solenoid increase when an iron core is placed in

its axis.

..

Electromagnetic induction:

Definition:

.

Parameters affect on the magnitude of induced electromotive force:

The magnitude of the induced electromotive force is

proportional to the rate of change in the magnetic field.

.. The induced electromotive force is proportional to the

number of turns N.

..Faradays law:

tN

=

Where:

: is .

: is .

t: is .

N: is

The negative sign indicates that:



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Faradays law statement:

..

Lenzs law:

To illustrate Lenzs law, a magnet bar can be pulled and pushed into a coil,

and by using of a galvanometer; the

direction of current can be indicated.

In figure A:

The North Pole of the magnet

pushed into the coil, therefore the direction of the induced current at the face of the

coil close to the magnet is forming . Pole to resist the

change of the magnetic field resultant by pushing of the magnet bar. (N N repel).

In figure B:

The North Pole of the magnet pulled from the coil; therefore the direction of

the induced current at the face of the coil close to the magnet is

forming . Pole to resist the change of the magnetic field resultant by

pulling of the magnet bar. (N S attract).

In figure C:

The South Pole of the magnet pushed into the coil; therefore the direction of


forming Pole to resist the change of the magnetic field resultant by pushing

of the magnet bar. (S S repel).



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In figure D:

The South Pole of the magnet pulled from the coil, therefore the direction of


forming .. Pole to resist the change of the magnetic field resultant by pulling

of the magnet bar. (N S attract).

Lenzs rule statement:

..

What is the direction of the induced current in the face of solenoid moved

towards the North Pole of U-shaped magnet?

..

Direction of the induced current in a straight wire:

When a current carrying wire is placed in magnetic field; force of motion

is result and its direction indicates by using of

...

When a straight wire moves in a magnetic field, an induced electromotive

force and induced current follow through the wire and the direction of

that current indicates by using of ....

Flemings right-hand-rule:



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A car moves from east to west raising its antenna, what is the direction of

the electric current in that antenna.

..

What is the benefit of each of the following:

Ampere right hand rule:

..

Lenzs law:

..

Flemming right hand rule:

..

Flemming left hand rule:

..

Mutual induction between two coils:

Induce electromotive force is produced when

The variable magnetic field may produce due to .

or ..

If the induce electromotive force is produced due to variable magnetic

field resulting from coil of current I, therefore, the induce electromotive



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force will be .. Proportional to the rate of change of that

current.

.............2

t

IM

1

2

=

Where:

M is .

(-ve) sign: ..

Mutual inductance coefficient between two coils:

M = .. or ...

Definition:

.. ..

.

Unit: or or

...

Factors affected on the mutual inductance between two coils:

1. ..

2. ..

3. ..

Experiments:

The change of magnetic field can be

caused as following:

To increase the field:

1.



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2.

3.

In this cases the magnetic field changes to increase its value, and the induced

current of the secondary coil will be in the direction to

To decrease the field:

1. .

2. .

3. .

In this cases the magnetic field changes to decrease its value, and the induced

current of the secondary coil will be in the direction to .

Example:

A solenoid coil of 200 turns, the cross sectional area of each turn equals 2

cm2; it is placed normally to a magnetic field of flux density 0.6 w/m2. Calculate the

induced e.m.f. for the cases when:

a) Flux density increases to 0.8 tesla in 2 x 10-3 sec.

b) The coil is turned back in 0.1 sec

....

....

....

....

[-4 volts, -0.48 volts]



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Self-induction of a coil:

When switching the key (on/ off), the

fluorescent lamp will not glow.

When switching the key (on / off), the

neon lamp will glow. (Required 180

Volts, while the battery is only 6

Volts).

Conclusion:

Switch on:

The main current of the coil will (increase / decrease) due to

..

The change of current in each turn cause .. in the

neighborhood turn.

The induced induction due to all the turns will be to resist the

of the main current of the coil. So, it will (increase / decrease) the total

electromotive force, which is (enough / not large enough) to glow the

florescent lamp.

Switch off:

The main current of the coil will (increase / decrease) due to

..

The change of current in each turn cause .. in the

neighborhood turn.

The induced induction due to all the turns will be to (increase / decrease)

the total current of the coil. So, it will (increase / decrease) the



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electromotive force to be (enough / not large enough) to glow the

fluorescent lamp.

The induction in this case called ., and the self-induced

electromotive force will be directly proportional to

.. = ..

Where:

: is .

I: is .

T: is .

L: is .

(-ve) sign: .

Self-induction coefficient of a coil (L):

Rule: .

Definition: .

.

Unit: or or

..

Henry:

Definition:

Unit: or

..



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Factors affect on the self-inductance of a coil:

G.R.:

TV set must switched off before get the blug out of electric source.

..

The Ohmic resistances are made of double wounded wires.

..

N.B.:

Problems of self induction can be solved by using of the rules:

..

Problems of mutual induction can be solved by using of the rules:

..

Example:

A solenoid has 200 turn and connected to battery of 2 A to produce magnetic

flux of 5x10-5 Weber, 70% of that field reaches another solenoid which has 800 turn

and its resistance is 40. Find both of self induction coefficient and mutual induction

coefficient, then if the current is vanished in 10 millisecond, find the total e.m.f in

both of the coils and the electric current pass through the second coil.



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.

Application of self induction:

The most common application of self induction is the function of

. lamp, and in Ruhmkorff coil, which is used as an ignition coil in

..

Fluorescent lamp:

It consists of tube contains amount of .. gas, and

its inner walls painted with .. material.

The electric energy stored in a coil outside the lamp in form of

energy.

The energy discharged in the lamp, casing the atoms of the inert gas to

. and collide with . and .. of the

tube.

As a result of .. the florescent material

..

Eddy currents:

If an alternated current pass through a conductor, it will cause continues

change in the magnetic field.

The change in the magnetic field through solid conductor produce

...



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L

X


The induced current in the solid conductor will be in form of .

and called ..

This phenomenon can be used to build the induction furnaces, which are

used in ...

Question:

How to avoid the eddy current.

.

E.M.F. induced in a moving straight wire:

If straight wire of length (L) moves with

velocity (V) in a magnetic field for interval

of time (T), it will cover an area of L X.

(where X is the distance covered by the

wire).

t

=

......

......B =

.........=

........A =

............=

t

XBL

t

XBL

t

=

=

=

..................=

BLV=

If the angle between the wire and the flux line is



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= sinBLV

Example:

Straight line wire of length 5 cm moves with a velocity of 25 m/s in a

magnetic field of intensity 7x10-5 Tessla. Calculate its electromotive force.

[8.75x10-5 V]

Alternating current:

Definition: .

Alternating current generator:

It is a device to generate Alternating

current.

Structure:

1. A field magnet:

2. An armature:

..

..

..

3. Slip rings with brushes:

..



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..

The mechanism of the generator:

The coil rotates itself between the magnet poles, therefore the velocity prefer

to be angular velocity .

f2

2

t

r

V ====

Where:

: is

V: is

F: is

The induced E.M.F in one-side equals: x x ..

But the coil consists of two sides connected in series, therefore:

E =

to convert the velocity from liner velocity into angular velocity V = .

Therefore; E =

But A =

Therefore; E =

In case of N turns:

E = .

or:

E = B A N sin



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Where:

is the angle between the magnetic flux line and the direction of motion

of the coil. or it is the angle between the magnetic flux line and the

perpendicular to the coil.

If equals to zero the coil is .. to the field and E.M.F equals

...

If equals 90 the coil is .. to the field and E.M.F equals

.

N.B.:

Unit of is .. and = . in calculating sin() or sin (

t)

Unit of is . and = . in calculating () or () out of

sin.

Instantaneous e.m.f:

The instantaneous E.M.F can be calculated from the relation

E = Eo sin I = Io sin

Where:

Eo is the maximum E.M.F.

Io is the maximum current.



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Figure A:

The coil is (perpendecular/ parallel) to the flux lines.

The direction of motion of

each side (perpendecular/

parallel) to the flux lines.

is equal .

E = (rule) .

E = (value) ..

Figure B:





is equal .

E = (rule) .

E = (value) ..

Figure C:





is equal .

E = (rule) .

E = (value) ..



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Figure D:


The direction of motion of each

side (perpendecular/ parallel) to

the flux lines.

is equal .

E = (rule) .

E = (value) ..

N.B.:

The E.M.F can be drawn in a sin curve as following:

Example:

The coil of a simple AC generator consists of 100 turns, the cross sectional

area of each is 0.21 m2. The coil rotates with frequency 50 Hz (cycle /second) in a

magnetic field of constant flux density B = 10-3 tesla. What is the maximum induced

E.M.F. generated? And what is instantaneous value at = 30? Then find the e.m.f

after 0.1 sec and find the time when the e.m.f becomes 5 volt.


A

B

C

D

E

t


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[6.6 V, 3.3V, 0, 2.7x10-3]

Effective values of the alternating current and voltage:

Since the value of the alternating current intensity is changes from (I)

maximum to (I) maximum; therefore the mathematical average equal

.

For that reason, the average can be calculated by calculate its heat effect.

Effective value of alternating current:

Definition:

Ieff= (Rule) .

Eeff= (Rule) ...

N.B.:

The average electromotive force can be calculated by using of faradays law

tN

=

The average electromotive force for a complete cyclee = zero (G.R.)

The average electromotive force for half cycle = the average of quarter

cycle and can be calculated from faradays law.

Where:

=


V

t


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t =

Example:

An electric current of intensity 2 amp in a coil of 400 turns, the produced

flux is 10-4 Webber. Calculate the average produced e.m.f in the coil when

the current vanishes in 0.08 sec. also calculate the self-induction of the

coil.

[0.5 volt, 0.02 H]

Current rectification in the dynamo:

To produce direct current, the two slip rings of the generator must replaced

with commentator (rectefier), which consists of

, each of the two halves attach to .. The two brushes replaced

position each ...

The direction of the electric

current will be ..,

while the magnitude of the E.M.F.

and the magnitude of the current will be vary from . to .. through each

quarter cycle as shown in the graph.

By using of two coils

perpendicular to each other the

current will be smoother as shown in the figure.


V

t

V

t


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To obtain steady value of

electric current intensity the coil must

replaced with .

and the commentator will

..

Example:

If the effective intensity of current in a circuit equals 10 amperes and the

effective voltage is 240 volts. What is the maximum value for each of current and

voltage?

[14.14 A, 340 V]

Transformer:

It is a device used to ...

Since the value of power is constant therefore when the voltage steps up

the current intensity will ., and that will decrease the

. while transfers electricity for a long distance.

The idea of transformer depends on .

G.R.:

Transformer is used only with AC current.

.

..


V

t


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Structure:

.

.

When the primary coil connected to a source of AC, the potential

deference between its terminal can be calculated from the relation

(according to faradays law):

...................VP=

)1.....(..............................

................

...............

N

V

P

P =

The potential deference between the terminal of the secondary coil can be

calculated from the relation (according to faradays law):

.......................VS=

)2.....(...........................................

.............

N

V

S

S =

From 1 & 2:

..............

.............

V

V

P

S =

P

P

SS V

N

NV =

In general some of the electric energy is converted into heat energy and

the rest of the percentage is convert into electric energy in the secondary

coil.

( ) PP

S

S VN

NyelectricitofusedV %=

The relation between IS & IP:

Energy is neither created nor destroyed.



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Energy of the primary coil = .

Energy of the secondary coil = .

Therefore: VP IP T =

VP IP = ..

...........

...........

I

I

P

S =

The loosing of energy in the transformer:

Some of the electric energy will loss in the transformer because of the

following:

A part of electric energy is converted into thermal energy in the wire of

coils.

It is recommended to

.

A part of the electric energy is converted into thermal energy in the soft

iron core.


.

Some of the energy is converted into mechanical energy (F = BIL) to

move the molecules of the soft iron.


.



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The efficiency of the transformer ():Definition: or .

Rule: .

Usage of transformer:

Heat energy is directly proportional to the square of the electric intensity.

W =

From Ohms law: V =

W =

During transfer the electric energy part of it will convert into

due to .. therefore it is preferred to use

(low / high) voltage with (low / high) current during transfer the electric

energy for along distance.

Step (up / down) transformer is used at the power station (power plant) to

(increase / decrease) the voltage and (increase / decrease) the current.

Step (up / down) transformer is used at the distribution regions to

(increase / decrease) the voltage and (increase / decrease) the current.

This will (increase / decrease) the loss of electric energy in form of heat

energy during the transfer.

Comparison between the step up and step down transformer:

Item Step up

transformer

Step down

transformer

Number of turns

Ratio between Pd of primary to

that of secondary coil



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Ration between I of primary to

that of secondary coil

Using

N.B.:

If the efficiency of transformer () equals 100% then

s

P

p

s

p

s

I

I

N

N

V

V==

If the efficiency of transformer () is less than 100% then

pp

s

s VN

N

V =

pp

ss

VI

VI=

Examples:

1. A transformer, when connected to a 240 volts power source, gives 900

volts output electromotive force with current intensity 4 amperes. What is

the intensity of the source current assuming that the efficiency of the

transformer is 100%?

..

..

..

[15A]

2. An electric ring is connected to a transformer of efficiency 80% which

gives 8 volts output, if the input voltage in the house is 240 volts what is

the number of turns of the secondary coil if the number of turns of the

primary coil is 1100 turns? And what is the intensity of current in the

secondary coil if the current in the primary coil is 0.1 ampere?



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..

..

..|

[46, 2.4 A]

The electric motor:

It is a device to convert the

energy into energy.

Structure:

.

When the coil is parallel to the magnetic field; the angle between the coil

and the magnetic flux line is .., the coil affected by torque of (rule)

. which equal to (value) .. and rotate between the

two poles of the magnet.

When the coil is perpendicular to the magnetic field; the angle between

the coil and the magnetic flux line is .., the coil affected by torque

force of (rule) . which equal to (value) .. but it

will rotate due to its inertia.



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Increasing the motors power:

Number of coils may be used with equal angles between their planes to

increase the power of the motor, and the cylinder is splited into number

of sections equal ..

Uniformity of rotation rate of the electric motor coil:

The torque reaches its maximum value when the plane of the coil is

, and that (increases / decrease) the angular velocity

of the coil.

The torque reaches its minimum value when the plane of the coil is

, and that (increases / decrease) the angular velocity

of the coil.

When the coil start to rotate the angel between the plane of the coil and

the field will changes from .. to . and that causes the

angular velocity to changes each ..

Although the previous two points but the angular velocity of the coil is

uniform due to the self-induction.

The induced current will be maximum when the coil is . to

the field, then the induced current will (increase / decrease) gradually by

the rotation of the coil.

The reverse current generated due to the self-induction of the coil

decrease the total current in the coil when the coil tends to increase its

speed.

W k Sh t 2008/2009

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wu4c11 by Adel Khamis