Class 10 MAGNETIC FIELD AND FIELD LINES AND MAGNETIC FIELD DUE TO A CURRENT-CARRYING CONDUCTOR

### Topic covered

color{red} ♦ INTRODUCTION
color{red} ♦MAGNETIC FIELD AND FIELD LINES
color{red} ♦ MAGNETIC FIELD DUE TO A CURRENT-CARRYING CONDUCTOR

### INTRODUCTION

We know that an electric current-carrying wire behaves like a magnet. Let us perform the following Activity to reinforce it.

ul"Activity 13.1"
♦ Take a straight thick copper wire and place it between the points X and Y in an electric circuit, as shown in Fig. 13.1.
♦ Place a small compass near to this copper wire. See the position of its needle.
♦ Pass the current through the circuit by inserting the key into the plug.
♦ Observe the change in the position of the compass needle.

We see that the needle is deflected. It means that the electric current through the copper wire has produced a magnetic effect.

Thus we can say that electricity and magnetism are linked to each other. Then, what about the reverse possibility of an electric effect of moving magnets?

So, Here we will study magnetic fields and such electromagnetic effects. We shall also study about electromagnets and electric motors which involve the magnetic effect of electric current, and electric generators which involve the electric effect of moving magnets.

### MAGNETIC FIELD AND FIELD LINES

We are familiar with the fact that a compass needle gets deflected when brought near a bar magnet. A compass needle is, in fact, a small bar magnet.

The ends of the compass needle point approximately towards north and south directions. The end pointing towards north is called north seeking or north pole. The other end that points towards south is called south seeking or south pole.

Through various activities we have observed that like poles repel, while unlike poles of magnets attract each other.

ul"Activity 13.2"

♦ Fix a sheet of white paper on a drawing board using some adhesive material.
♦ Place a bar magnet in the centre of it.
♦ Sprinkle some iron filings uniformly around the bar magnet (Fig. 13.2). A salt-sprinkler may be used for this purpose.
♦ Now tap the board gently.
♦ What do you observe?

The iron filings arrange themselves in a pattern as shown Fig. 13.2. Why do the iron filings arrange in such a pattern? What does this pattern demonstrate?

The magnet exerts its influence in the region surrounding it. Therefore the iron filings experience a force. The force thus exerted makes iron filings to arrange in a pattern.

The region surrounding a magnet, in which the force of the magnet can be detected, is said to have a magnetic field. The lines along which the iron filings align themselves represent magnetic field lines.

Are there other ways of obtaining magnetic field lines around a bar magnet? Yes, you can yourself draw the field lines of a bar magnet.

ul"Activity 13.3"

♦ Take a small compass and a bar magnet.
♦ Place the magnet on a sheet of white paper fixed on a drawing board, using some adhesive material.
♦ Mark the boundary of the magnet.
♦ Place the compass near the north pole of the magnet. How does it behave? The south pole of the needle points towards the north pole of the magnet. The north pole of the compass is directed away from the north pole of the magnet.
♦ Mark the position of two ends of the needle.
♦ Now move the needle to a new position such that its south pole occupies the position previously occupied by its north pole.
♦ In this way, proceed step by step till you reach the south pole of the magnet as shown in Fig. 13.3.

♦ Join the points marked on the paper by a smooth curve. This curve represents a field line.
♦ Repeat the above procedure and draw as many lines as you can. You will get a pattern shown in Fig. 13.4. These lines represent the magnetic field around the magnet. These are known as magnetic field lines.

♦ Observe the deflection in the compass needle as you move it along a field line. The deflection increases as the needle is moved towards the poles.

Magnetic field is a quantity that has both direction and magnitude. The direction of the magnetic field is taken to be the direction in which a north pole of the compass needle moves inside it.

Therefore it is taken by convention that the field lines emerge from north pole and merge at the south pole (note the arrows marked on the field lines in Fig. 13.4). Inside the magnet, the direction of field lines is from its south pole to its north pole.

Thus the magnetic field lines are closed curves.

The relative strength of the magnetic field is shown by the degree of closeness of the field lines. The field is stronger, that is, the force acting on the pole of another magnet placed is greater where the field lines are crowded (see Fig. 13.4).

No two field-lines are found to cross each other. If they did, it would mean that at the point of intersection, the compass needle would point towards two directions, which is not possible.

### MAGNETIC FIELD DUE TO A CURRENT-CARRYING CONDUCTOR

In Activity 13.1, we have seen that an electric current through a metallic conductor produces a magnetic field around it.

In order to find the direction of the field produced let us repeat the activity in the following way :-

ul"Activity 13.4"

♦ Take a long straight copper wire, two or three cells of 1.5 V each, and a plug key. Connect all of them in series as shown in Fig. 13.5 (a).
♦ Place the straight wire parallel to and over a compass needle.
♦ Plug the key in the circuit.
♦ Observe the direction of deflection of the north pole of the needle. If the current flows from north to south, as shown in Fig. 13.5 (a), the north pole of the compass needle would move towards the east.
♦ Replace the cell connections in the circuit as shown in Fig. 13.5 (b). This would result in the change of the direction of current through the copper wire, that is, from south to north.
♦ Observe the change in the direction of deflection of the needle. You will see that now the needle moves in opposite direction, that is, towards the west [Fig. 13.5 (b)]. It means that the direction of magnetic field produced by the electric current is also reversed.

Q 3214691559

A current through a horizontal power line flows in east to west direction. What is the direction of magnetic field at a point directly below it and at a point directly above it?
Class 10 Chapter 13 Example 1
Solution:

The current is in the east-west direction. Applying the right-hand thumb rule, we get that the direction of magnetic field at a point below the wire is from north to south. The direction of magnetic field at a point directly above the wire is from south to north.

### Magnetic Field due to a Current through a Straight Conductor

What determines the pattern of the magnetic field generated by a current through a conductor? Does the pattern depend on the shape of the conductor? We shall investigate this with an activity.

We shall first consider the pattern of the magnetic field around a straight conductor carrying current.

ul"Activity 13.5"

♦ Take a battery (12 V), a variable resistance (or a rheostat), an ammeter (0–5 A), a plug key, and a long straight thick copper wire.
♦ Insert the thick wire through the centre, normal to the plane of a rectangular cardboard. Take care that the cardboard is fixed and does not slide up or down.
♦ Connect the copper wire vertically between the points X and Y, as shown in Fig. 13.6 (a), in series with the battery, a plug and key.

♦ Sprinkle some iron filings uniformly on the cardboard. (You may use a salt sprinkler for this purpose.)
♦ Keep the variable of the rheostat at a fixed position and note the current through the ammeter.
♦ Close the key so that a current flows through the wire. Ensure that the copper wire placed between the points X and Y remains vertically straight.
♦ Gently tap the cardboard a few times. Observe the pattern of the iron filings. You would find that the iron filings align themselves showing a pattern of concentric circles around the copper wire (Fig. 13.6).
♦ What do these concentric circles represent? They represent the magnetic field lines.
♦ How can the direction of the magnetic field be found? Place a compass at a point (say P) over a circle. Observe the direction of the needle. The direction of the north pole of the compass needle would give the direction of the field lines produced by the electric current through the straight wire at point P. Show the direction by an arrow.
♦ Does the direction of magnetic field lines get reversed if the direction of current through the straight copper wire is reversed? Check it.

What happens to the deflection of the compass needle placed at a given point if the current in the copper wire is changed? To see this, vary the current in the wire. We find that the deflection in the needle also changes.

In fact, if the current is increased, the deflection also increases. It indicates that the magnitude of the magnetic field produced at a given point increases as the current through the wire increases.

What happens to the deflection of the needle if the compass is moved from the copper wire but the current through the wire remains the same? To see this, now place the compass at a farther point from the conducting wire (say at point Q).

What change do you observe? We see that the deflection in the needle decreases. Thus the magnetic field produced by a given current in the conductor decreases as the distance from it increases.

From Fig. 13.6, it can be noticed that the concentric circles representing the magnetic field around a current-carrying straight wire become larger and larger as we move away from it.

### Right-Hand Thumb Rule

A convenient way of finding the direction of magnetic field associated with a current-carrying conductor is Imagine that you are holding a current-carrying straight conductor in your right hand such that the thumb points towards the direction of current.

Then your fingers will wrap around the conductor in the direction of the field lines of the magnetic field, as shown in Fig. 13.7. This is known as the right-hand thumb rule.

### Magnetic Field due to a Current through a Circular Loop

We have so far observed the pattern of the magnetic field lines produced around a current-carrying straight wire. Suppose this straight wire is bent in the form of a circular loop and a current is passed through it.

How would the magnetic field lines look like? We know that the magnetic field produced by a current-carrying straight wire depends inversely on the distance from it.

Similarly at every point of a current-carrying circular loop, the concentric circles representing the magnetic field around it would become larger and larger as we move away from the wire (Fig. 13.8).

By the time we reach at the center of the circular loop, the arcs of these big circles would appear as straight lines. Every point on the wire carrying current would give rise to the magnetic field appearing as straight lines at the center of the loop.

By applying the right hand rule, it is easy to check that every section of the wire contributes to the magnetic field lines in the same direction within the loop.

We know that the magnetic field produced by a current-carrying wire at a given point depends directly on the current passing through it.

Therefore, if there is a circular coil having n turns, the field produced is n times as large as that produced by a single turn. This is because the current in each circular turn has the same direction, and the field due to each turn then just adds up.

ul"Activity 13.6"

♦ Take a rectangular cardboard having two holes. Insert a circular coil having large number of turns through them, normal to the plane of the cardboard.
♦ Connect the ends of the coil in series with a battery, a key and a rheostat, as shown in Fig. 13.9.

♦ Sprinkle iron filings uniformly on the cardboard.
♦ Plug the key.
♦ Tap the cardboard gently a few times. Note the pattern of the iron filings that emerges on the cardboard.

### Magnetic Field due to a Current in a Solenoid

A coil of many circular turns of insulated copper wire wrapped closely in the shape of a cylinder is called a solenoid. The pattern of the magnetic field lines around a current-carrying solenoid is shown in Fig. 13.10.

Compare the pattern of the field with the magnetic field around a bar magnet (Fig. 13.4). Do they look similar? Yes, they are similar. In fact, one end of the solenoid behaves as a magnetic north pole, while the other behaves as the south pole.

The field lines inside the solenoid are in the form of parallel straight lines. This indicates that the magnetic field is the same at all points inside the solenoid. That is, the field is uniform inside the solenoid.

A strong magnetic field produced inside a solenoid can be used to magnetise a piece of magnetic material, like soft iron, when placed inside the coil (Fig. 13.11). The magnet so formed is called an electromagnet.