Chapter 9.3 - Fleming's Left hand Rule

In the previous section we saw that, a current carrying solenoid will act as a bar magnet. We also saw the methods to increase the strength of it's magnetic field. In this section, we will see Fleming's Left hand rule.
• In the discussions so far in this chapter, we can notice the following peculiarity:
    ♦ The current carrying conductor was stationary. That is., it was fixed in a position
    ♦ The magnet was free to move
• Now we will consider the opposite situation:
    ♦ The magnet is stationary
    ♦ The current carrying conductor is free to move.
Let us do an activity. We will write it in steps:
1. In fig.9.19(a) given below, a U shaped magnet is kept stationary in a vertical position

Fig.9.19

• A straight aluminium conductor AB is suspended midway between the N and S poles of the magnet
• AB is suspended using thin wires. So it can oscillate freely
2. The thin wires are both connected to a battery through a switch
• End A is connected to the positive terminal of the battery. So current flows from A to B
3. The switch is turned on.
• The conductor is suddenly displaced to one side. 
• The displacement is towards the magnet. This is shown in fig.b
■ We can say: When the magnet is stationary and conductor is movable, that conductor will move when current passes through it
■ In the previous activities we saw this: When the magnet is movable and conductor is stationary, the magnet will move when current passes through the conductor
• But what we see in fig.9.19(b) above is only one of the four possible cases. Let us see the other three:
4. Case 2: In fig.9.20 below, all the arrangements are the same as in case 1 except that, the connections to the terminals of the battery are interchanged.

Fig.9.20

• So when the switch is turned on, the current will flow from B to A in the conductor. 
• We can see that, AB is now displaced away from the magnet
5. Case 3: In fig.9.21(a) below, all the arrangements are the same as in case 1 except that, the north and south poles of the magnet are interchanged. The N pole is now at top and S pole is at bottom. 

Fig.9.21

• When the switch is turned on, the current will flow from A to B in the conductor. 
• We can see that, AB is now displaced away from the magnet
6. Case 4: In fig.9.21(b) above, all the arrangements are the same as in case 3 except that, the connections to the terminals of the battery are interchanged.
• So when the switch is turned on, the current will flow from B to A in the conductor. 
• We can see that, AB is now displaced towards the magnet

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We can write a summary:
Case 1: 
■ North pole above and South pole below
• Current from A to B
    ♦ Conductor AB moves towards the magnet
Case 2:
■ North pole above and South pole below
• Current from B to A
    ♦ Conductor AB moves away from the magnet
Case 3:
■ North pole below and South pole above
• Current from A to B
    ♦ Conductor AB moves away from the magnet
Case 4:
■ North pole below and South pole above
• Current from B to A
    ♦ Conductor AB moves towards the magnet

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From the above four cases, we can infer the following points:
(i) A force is acting on the conductor. That is why it is being displaced
(ii) The direction of the force depends on the direction of the current. 
(iii) The direction of the force depends on the direction of the magnetic field
■ So the direction of the force depends on two quantities:
• Direction of current
• Direction of magnetic field

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■ Suppose a person shows us the poles of a magnet and also a conductor AB between those poles. 
Then he asks us: If current flows from A to B, in which direction will the conductor move?
• To answer such questions, we can use a special rule known as Fleming's left hand rule:
Hold the forefinger, middle finger and thumb of the left hand in mutually perpendicular directions as shown in the fig.9.22 below:

Fig.9.22 Source: Wikimedia commons

IF
Forefinger indicates the direction of the magnetic field B
AND
Middle finger indicates the direction of the current I
THEN
The thumb will indicate the direction of force F

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The following points should be noted while using this rule:
• Only left hand should be used. If we use the right hand, required results will not be obtained
• The forefinger, middle finger and thumb should be kept perpendicular to each other

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• A 3D model of the fingers is shown in the fig.9.23 below:

Fig.9.23

• The advantage of making such a model is that, it can be aligned to any required direction that we want

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Let us now apply the model to the four cases that we saw above. 
Case 1:
1. Consider fig.9.24 below:

• Direction of the magnetic field is always from the north pole to south pole. So the forefinger is pointing upwards
2. Current is flowing from A to B. The middle finger in the model is pointing in this direction
3. When the above two directions are fixed, there is only one possible direction in which the thumb can point
• The conductor AB is indeed moving in that direction of the thumb

Case 2:
1. Consider fig.9.25 below:

Fig.9.25

• Direction of the magnetic field is always from the north pole to south pole. So the forefinger in the model is pointing upwards
2. Current is flowing from B to A. The middle finger in the model is pointing in this direction
3. When the above two directions are fixed, there is only one possible direction in which the thumb can point
• The conductor AB is indeed moving in that direction of the thumb

Case 3:
1. Consider fig.9.26 below:

Fig.9.26

• Direction of the magnetic field is always from the north pole to south pole. So the forefinger in the model is pointing downwards
2. Current is flowing from A to B. The middle finger in the model is pointing in this direction
3. When the above two directions are fixed, there is only one possible direction in which the thumb can point
• The conductor AB is indeed moving in that direction of the thumb

Case 4:
1. Consider fig.9.27 below:

Fig.9.27

• Direction of the magnetic field is always from the north pole to south pole. So the forefinger in the model is pointing downwards
2. Current is flowing from B to A. The middle finger in the model is pointing in this direction
3. When the above two directions are fixed, there is only one possible direction in which the thumb can point
• The conductor AB is indeed moving in that direction of the thumb

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In the next section we will see the basics of an Electric motor.

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Chapter 9.2 - The Solenoid

In the previous section we saw the current through a circular conductor. We also saw that, increasing the number of circular conductors will increase the strength of the magnetic field. In this section, we will see an activity to prove this.

1. Consider the circular conductor shown in fig.9.9(a) below. 

Fig.9.9

• The two points at which it pierces through the cardboard are named as A and B. 
• The conductor must be 'straight up'. That is., it must be perfectly vertical. 
• Also the cardboard must be perfectly horizontal.
2. The line through A and B should be aligned exactly in the North-South direction
3. The exact midpoint between A and B is named as C
• Through C, a perpendicular line XY is drawn
4. Place a magnetic needle exactly centred at C. This is shown in fig.b
[Note that, the magnetic needle should be mounted on a pivot. Then only it will rotate freely. In the fig. however, the pivot is not shown. Also the connections of the conductor to the battery is not shown in the fig. These are to avoid clutter and thus increase clarity]
5. Now we can turn on the switch. The current flows from A to B. This is shown in fig.9.10(a) below:

Fig.9.10

• The needle deflects towards the west. 
■ This is due to the force exerted by the circular conductor
6. Now gradually move the needle towards X. 
• The movement should be along the line XY
• We can see that the deflection gradually decreases. 
    ♦ The needle is moving back towards the normal North-South orientation. 
• This is because, as the distance from the conductor increases, the force exerted by it decreases.
7. Keep moving the needle. 
• We will reach a particular point at which the needle is back in the exact North-South orientation.
8. Mark this point as O₁. This is shown in fig.9.11(a) below:

Fig.9.11

• Measure the distance CO₁ and note it down. 
■ We can write: Beyond the point O₁, the conductor has no influence on the needle 
9. Turn off the switch. Add a second circular conductor parallel to AB. This is shown in fig.b. Repeat the experiment.
• Ensure that the current I is same as that in the previous trial. This can be done using a rheostat.
[It is important to ensure that the currents are the same. Because, we want to prove that, the magnetic field becomes stronger because of an additional conductor. It must not be due to the increase in current]
• Find the point O₂ and mark it. 
• O₂ is the point beyond which, the 'combined action the two circular conductors' have no influence on the needle. 
10. Measure the length of CO₂ and note it down
• We will see that, CO₂ is greater than CO₁ 
■ This is because, the combined action produced a stronger magnetic field. This stronger magnetic field can exert a force to a greater distance.
• If we add a third circular conductor, even if the current is the same, we will find that CO₃ is greater than CO₂

---

So we achieved our objective. We proved that:
■ Increasing the number of circular conductors will increase the strength of the magnetic field. 
• But now a problem arises:
We need to figure out a method to connect those circular conductors together. Then only the 'same current from a single battery source' will flow through them.
• Consider the conductor in fig.9.12(a) below:

Fig.9.12

• The current flowing upwards through end X will come downwards through the end Y. 
    ♦ This is possible because the conductor is wound in the form of a spring coil. 
• This coil can be made to pierce through a cardboard. It is shown in fig (b).
• When we look from above the cardboard, it will appear as two separate circular conductors. 
    ♦ But there is interconnection below the card board.
• If we want three circular conductors, one more turn can be added to the coil. This is shown in fig.9.13 below:

Fig.9.13

• In fact we can add a large number of turns. This is shown in fig.9.14 below:

Fig.9.14

 ■ When the 'number of turns' of the coil is increased, the strength of the magnetic field is increased.
• Such a coil is indeed used in many electrical devices. It is called a solenoid. 
Some images can be seen here.
• It is used in situations where a strong magnetic field is required. 
■ The official definition is:
Solenoid is a conducting coil wound in the shape of a spring.

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• We know that each individual turn of the solenoid will have it's own magnetic field. 
• So the fields of adjacent turns will combine together to give a strong magnetic field
• The fig.9.15 below shows a comparison between the following two items:
(a) The magnetic field lines around a solenoid  
(b) The magnetic field lines around a bar magnet

Fig.9.15

• The details of the solenoid in the above fig. is obtained from wikimedia commons here 
• The details of the bar magnet in the above fig. is obtained from wikimedia commons here 
■ Comparing the two, we can see that, they are identical. 
That is.,
• The magnetic field lines around a solenoid
Is identical to:   
• The magnetic field lines around a bar magnet

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So a current carrying solenoid will act as a bar magnet. Our next task is to find it's poles
There are 3 methods to find the poles. They are described below:
Method 1:
• Bring a magnetic needle near one end of the current carrying solenoid
    ♦ If the north pole of the needle gets attracted, then that end of the solenoid is it's south pole  
    ♦ If the south pole of the needle gets attracted, then that end of the solenoid is it's north pole  
Method 2:
We will write this method in steps:
1. Consider the solenoid in fig.9.16 (a) below:

Fig.9.16

• The current goes up through X and comes down through Y
2. Imagine we are standing at the tail end of the cyan arrow. And we are looking towards the head end of the cyan arrow
• We will see that, the current I is flowing in the clockwise wise direction
3. Imagine we are standing at the tail end of the red arrow. And we are looking towards the head end of the red arrow
• We will see that, the current I is flowing in the anti-clockwise wise direction
4. The opposite of the above two will happen when the current is reversed. This is shown in fig.b
• At end X, the the current is flowing in the anti-clockwise direction. 
• And at end Y, the current is flowing in the clockwise direction.
5. So we find an important property: 
■ Even if current is flowing normally from one end of the solenoid to the other end, when looked from either ends, one is clockwise and the other is anti-clockwise. 
• This property can be related to the polarity. The rule is:
(i) Hold a solenoid against your face. 
(ii) Note the direction of current at the end nearest to your face. 
• If the direction is clockwise, then that end is the south pole.
• If the direction is anti-clockwise, then that end is the north pole.
Method 3:
1. Consider the solenoid in the above fig.9.16(a). 
• Imagine that the following two conditions are satisfied:
(i) You are holding it in the right hand. 
(ii) The thump is pointing towards the end X. 
2. If the above two conditions are satisfied, the other fingers will be pointing in a 'direction opposite to the direction of current'. 
• Such an 'opposite pointing' is not allowable for this method to work
• We want 'pointing in the same direction'. So what do we do?
3. Note that, only right hand should be used. Let the thumb point towards Y. We will write the steps again: 
• Imagine that the following two conditions are satisfied:
(i) You are holding it in the right hand. 
(ii) The thump is pointing towards the end Y. 
4. If the above two conditions are satisfied, the other fingers will be pointing 'in the same direction of current'.     
• So this is acceptable. 
• In this situation, the end towards which the thumb points is the north pole.
So we can write a summary of this third method:
■ Imagine the solenoid being held by the right hand. If the four fingers encircling the solenoid shows the direction of the current, the thumb indicates the north pole.

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So we have seen the basic properties of a solenoid. Now we will see methods to increase the magnetic strength of a solenoid.
Method 1:
• We know that the solenoid has a large number of turns. 
• We have also seen that, when current is turned on, 'a combination of magnetic fields' of the individual turns takes place. 
• So if the 'number of turns' is increased, the strength of the magnetic field will increase.
Method 2:
• Use a soft iron core. Let us see how it is done:
• We know that the solenoid has a large number of turns. 
• If these turns are made around a soft iron core, then the strength of the magnetic field will increase. This is shown in the fig.9.17 below:

Fig.9.17 Source: Wikimedia commons

■ The following properties of soft iron makes it suitable for the core:
• It has greater magnetic susceptibility
    ♦ That is., soft iron is 'attracted more' into a magnetic field than other metals  
• It has greater magnetic permeability
    ♦ That is., soft iron has a greater 'tendency to support the formation of magnetic fields within it's body' than other metals

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Now we will see the working of a Miniature Circuit Breaker, which is commonly known as MCB.

We will write it in steps:
1. In the fig.9.18(a) below, for the bulb to glow, current must flow from A to B. 

Fig.9.18

2. But between A and B, a MCB is placed. 
• The cyan rectangle shows the body of the MCB. 
• The circuit will be complete only if the current successfully come out of the MCB. 
3. The current entering the MCB is lead to the coil shown in red colour. 
• So the current flows through all the turns of the coil. 
• A soft iron core is placed inside the coil. 
• The current emerging from the coil passes through the conductor shown in green colour. 
• After passing through the green conductor, the current emerges from the MCB and flows into the bulb. Thus the circuit is completed. 
4. But when there is a fault in the circuit as shown in fig.b, or when there is an over load, excess current flows through the circuit. 
• Then a strong magnetic field is developed in the coil. 
• The soft iron core will get magnetized. That is., the soft iron core will become a temporary magnet. 
• So it will be attracted towards the green conductor. Because of the forward motion of the soft iron core, the green conductor will be displaced from it's original position. 
• Thus the circuit will break. Current will no longer flow through the circuit.

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In the next section we will see some basics about the Electric motor.

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Chapter 9.1 - Magnetic field around Current carrying Conductor

In the previous section we we saw that there will be an interaction between a current carrying conductor and a magnet. In this section, we will discuss about it's details.

• We know that, a magnetic field will exert a force on another magnet. 
• In our present case, we have a ready magnet. It is the magnetic needle. 
• A new magnetic field acted upon this magnetic needle. 
■ Where did this new magnetic field come from?  
Ans: Whenever current passes through a conductor, a magnetic field is developed around it. 
In our present case, when the switch was turned on, current passed through AB and so a magnetic field was developed around AB.

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Let us learn more about this new magnetic field. We will learn it with the help of an activity:
1. Insert a conductor AB through the centre of a cardboard as shown in fig.9.3(a) below:

Fig.9.3

• The conductor should be in a vertical position. 
2. Turn the switch on and allow current to pass through the conductor. 
3. Using a magnetic compass or magnetic needle, draw the magnetic field lines around the conductor. 
The method of drawing can be seen here.
• When we view the cardboard from the top, we will see that the magnetic lines are in the anti-clockwise direction. 
• Note that, positive terminal of the battery is connected to the lower end A of the conductor. So current flowed from bottom A to top B
4. Now use another cardboard. This time, the lower end A of the conductor should be connected to the negative terminal of the battery. So the current will flow from the top B to bottom A. 
5. Draw the magnetic field lines around the conductor. We will see that the lines are in the clockwise direction. This is shown in fig.9.3(b) 

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From the above activity the following two items are evident:
Item I: A magnetic field exists around a current carrying conductor
• Note that the cardboard can be placed at any point along the length of the conductor. We will get the same lines of force. 
• That means, the same lines of force exists along the whole length of the conductor. 
• So all the magnetic lines taken together will take the form of a cylinder. 
This is shown in the fig.9.4 (a) below:

Fig.9.4

• If a magnet comes anywhere near that cylinder, 'an interaction' will take place.
Item II: The direction of the magnetic field depends upon the direction of the current.

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• Since the direction depends on the direction of the current, we may encounter situations such as the one described below:
• A person shows us a wire AB. Then he asks:
• If current flows from A to B, what will be the direction of the magnetic field lines?
• A special rule known as Right hand thumb rule will help us to give the answer.
■ Imagine you are holding a current carrying conductor with the right hand in such a way that  the thumb points in the direction of the current. The direction in which the other fingers encircle the conductor gives the direction of the magnetic field. This is the Right hand thumb rule. It is shown in fig.9.4(b) above.
• To get a better understanding of the rule, we will break it down into simpler sentences:
1. Hold the current carrying conductor in the right hand. 
• Holding in the left hand will not give the required results
2. The thumb should point in the direction of the current. 
3. The other four fingers should encircle the conductor. 
4. Then the direction indicated by the other four fingers will give the direction of the magnetic field lines
5. Fig.9.4(c) shows the application of the rule when the current flows from top to bottom

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Next we are going to see a special case. We will write it in steps.
1. Consider fig.9.5 below:

Fig.9.5

• Two current carrying conductors are kept side by side. 
• The current is flowing in the same direction (bottom to top) in both of them. 
• The magnetic field around each conductor is also drawn. 
2. Now let us view the conductors in a direction shown by the cyan arrow. 
• That is., we are standing at the tail end of the cyan arrow and looking towards the head of the arrow. 3. We can see an interesting situation:
• Look closely at the field lines between the two conductors
    ♦ The field lines of the left conductor are flowing away from us  
    ♦ The field lines of the right conductor are flowing towards us
• So the field lines between the two conductors are traveling in opposite directions. 
4. Is their any possibility to make them both travel in the same direction?
Let us try:
• In fig.9.6 below, the direction of current in the right side conductor is reversed. 

Fig.9.6

5. Now look closely at the field lines between the two conductors
    ♦ The field lines of the left conductor are flowing away from us  
    ♦ The field lines of the right conductor are also flowing away from us
• So the field lines between the two conductors are now traveling in the same direction.
6. In this situation, we get a 'special zone'
• This 'special zone' is the space between the two conductors. 
    ♦ It is 'special' because, the magnetic field here is 'stronger'
    ♦ It is 'stronger' because, the fields from two conductors are in the same direction.
7. In the fig.9.6, we are having two separate conductors. That means, we have to supply current separately to them. 
• Is there any possibility to make the same current I to flow through both of them? Let us try:
Consider fig.9.7 below:

Fig.9.7

• A conductor is bent into a circular shape. 
• It pierces the cardboard at two points. 
[The portion of the conductor below the cardboard will not be visible in the fig. So it is shown in dashed lines]
8. Connect it to a battery and turn on the switch
• At the left piercing point, the current is traveling from bottom to top 
• At the right piercing point, the current is traveling from top to bottom
• Now look closely at the field lines between the two piercing points
    ♦ The field lines on the left side are flowing away from us  
    ♦ The field lines on the right side are also flowing away from us  
• So the field lines between the two piercing points are traveling in the same direction. We have the 'special zone'
9. Now reverse the terminal connections to the battery and turn on the switch. 
• The current will flow in the opposite direction. This is shown in fig.9.7(b)
• Look closely at the field lines between the two piercing points
    ♦ The field lines on the left side are flowing towards us  
    ♦ The field lines on the right side are also flowing towards us  
• So the field lines between the two piercing points are traveling in the same direction. Thus in this case also, we have the 'special zone'.

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• Now we can try to improve this apparatus. That is, we want to 'increase the strength of the magnetic field'. 
• Of course, we can do it by increasing the intensity of the current. 
• But can we do it with the same current intensity? Let us try:
1. Consider fig.9.8(a) below. One more circular shaped conductor is piercing through the cardboard.

Fig.9.8

2. A magnetic field will be produced in between the new piercing points also. 
• This new magnetic field will have the same direction as the one already produced by the first circular conductor. 
    ♦ This is because, the currents are both in the same direction. 
• So the two magnetic fields will combine together. Thus we get a stronger magnetic field. 
3. If we place a third circular conductor, the magnetic field will become even more stronger. This is shown in fig,9.8(b)

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• So our next task is to prove this:
■ Increasing the number of circular conductors will increase the strength of the magnetic field. 
• We can prove it using an activity. We will see it in the next section.

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