NCERT Solutions Class 10 Science Chapter 12 — Magnetic Effects of Electric Current

NCERT Class 10 Science — Magnetic Effects of Electric Current, Chapter 12 Exercises. All 9 questions solved.

Also here. Solutions to the in-text questions for this chapter and the activities for this chapter are on their own pages.

The nine exercises at the end of Chapter 12 fall into three groups. Questions 1, 3(a) and 4 are about the magnetic field that a current produces and the shape of its field lines. Questions 5, 6 and 7 are about the force that a magnetic field exerts on a current, and about finding directions. Questions 2, 3(b), 8 and 9 are about the wiring in our homes and how it is kept safe. There is no arithmetic to do; almost everything runs on two rules and one law:

• Right-hand thumb rule — hold a current-carrying wire in your right hand with the thumb along the current; your fingers curl round the wire in the direction of the magnetic field lines.
• Fleming’s left-hand rule — stretch the thumb, first finger and second finger of your left hand so that they are at right angles to each other. If the first finger points along the magnetic field and the second finger along the current, the thumb points along the force on the conductor.
• Ohm’s law — $I = \dfrac{V}{R}$. With the supply voltage fixed at $220\ \text{V}$, the current is decided by the resistance of the path: the smaller the resistance, the larger the current.

Key insight. Every direction in this exercise comes from one of the two hand rules, and the only trap is using the wrong direction for the current. The current in these rules is the conventional current, which flows opposite to the way electrons move — that is the whole of Question 6. The safety questions (2, 8 and 9) are Ohm’s law in disguise: a short circuit leaves almost no resistance in the path, so the current becomes huge, and an earth wire gives any leaking current a path of almost no resistance that does not go through your body.

Question 1

Which of the following correctly describes the magnetic field near a long straight wire?

Solution. When iron filings are sprinkled on a card with a current-carrying wire passing straight through it (Activity 12.5 in the chapter), they arrange themselves in circles round the wire. Each circle lies in a plane at right angles to the wire, and all the circles have the wire at their centre. The circles get farther apart as we move away from the wire, because the field becomes weaker with distance. The direction round each circle is given by the right-hand thumb rule. In the figure below the current comes out of the page, towards you. Point your right thumb at yourself and your fingers curl anticlockwise, so the field lines run anticlockwise.

So the field is neither straight lines, as (a) and (b) say, nor lines spreading outwards from the wire, as (c) says; it is circles round the wire.

Question 2

At the time of short circuit, the current in the circuit

Solution. A short circuit happens when the live wire and the neutral wire touch each other directly, for instance where the insulation has worn away or inside a faulty appliance. The current then takes this short cut instead of flowing through the appliance, so the resistance in its path drops to almost nothing. The supply voltage stays at $220\ \text{V}$, so by Ohm’s law the current shoots up. As an example, an appliance of resistance $44\ \Omega$ normally draws

$$I = \frac{V}{R} = \frac{220\ \text{V}}{44\ \Omega} = 5\ \text{A}$$

but if a short circuit leaves only $0.1\ \Omega$ in the path, the current tries to become

$$I = \frac{220\ \text{V}}{0.1\ \Omega} = 2200\ \text{A}$$

A current that large heats the wires strongly and can start a fire, which is why the circuit has a fuse to cut it off.

Question 3

State whether the following statements are true or false. (a) The field at the centre of a long circular coil carrying current will be parallel straight lines. (b) A wire with a green insulation is usually the live wire of an electric supply.

Question 3 (a)

Solution. A long coil made of many circular turns is a solenoid. Inside a current-carrying solenoid the field lines are parallel straight lines, which means the field is the same at every point inside — it is uniform. Outside, the field lines leave one end, loop round and enter the other end, just like the field of a bar magnet. The end the lines leave acts as a north pole and the end they enter acts as a south pole.

The same is true even of a single circular loop. Near the wire the field lines are small circles round it, but they grow larger towards the middle of the loop, and by the time they reach the centre they are arcs of such big circles that they look like straight lines. Every part of the loop sends its field through the centre in the same direction, so the lines there are parallel. Either way, the statement is true.

Question 3 (b)

Solution. In the colour code used in the chapter, the live wire has red insulation, the neutral wire has black insulation, and the earth wire has green insulation. The green wire is the safety wire that connects the metal body of an appliance to the earth; it is not the live wire. (The international code uses brown for live, blue for neutral and green-and-yellow for earth — in either scheme, green marks the earth wire.)

Question 4

List two methods of producing magnetic fields.

Solution. The chapter shows two sources of a magnetic field. The first is a magnet: a bar magnet or a horse-shoe magnet has a field round it all the time. The second is an electric current: any wire carrying a current has a magnetic field round it, whether it is a straight wire, a circular coil or a solenoid. Winding the wire into a solenoid and putting a soft iron core inside gives an electromagnet, a strong magnet that can be switched on and off with the current.

Question 5

When is the force experienced by a current–carrying conductor placed in a magnetic field largest?

Solution. In Activity 12.7 an aluminium rod carrying a current is hung between the poles of a horse-shoe magnet, and it is pushed sideways. The chapter reports that the push, and so the displacement of the rod, is largest when the current in the rod is at right angles to the magnetic field. If the rod is turned so that the current runs along the field lines, the force becomes zero. For a given angle, the force is also larger when the current is larger or the magnet is stronger.

Question 6

Imagine that you are sitting in a chamber with your back to one wall. An electron beam, moving horizontally from back wall towards the front wall, is deflected by a strong magnetic field to your right side. What is the direction of magnetic field?

Solution. Fleming’s left-hand rule is stated for the direction of the current, and current is taken to flow opposite to the way electrons move. The electrons move from the back wall towards the front wall, so the current they make flows from the front wall towards the back wall — towards you. Now fit the rule to what we know:

• the force (thumb) points to your right, because that is the way the beam is pushed;
• the current (second finger) points towards the back wall, towards you;
• the first finger then points straight down.

Try it with your left hand: point the thumb to your right and the second finger back at yourself, and the first finger points at the floor. So the magnetic field is vertically downwards.

The figure shows the chamber from above. Looking down from the ceiling, a field pointing downwards goes into the page, so it is drawn as crosses. Check it with the rule: first finger into the page (down), second finger towards the back wall (the current), and the left thumb points to your right, the way the beam bends.

Question 7

State the rule to determine the direction of a (i) magnetic field produced around a straight conductor-carrying current, (ii) force experienced by a current-carrying straight conductor placed in a magnetic field which is perpendicular to it, and (iii) current induced in a coil due to its rotation in a magnetic field.

Question 7 (i)

Solution. The field lines round a straight wire are circles (Question 1), and the rule has to say which way round they go. Imagine holding the wire in your right hand with your thumb pointing in the direction of the current. Your fingers wrap round the wire in the direction of the magnetic field lines. The same rule is also called Maxwell’s corkscrew rule: if a corkscrew is driven in the direction of the current, it turns in the direction of the field.

Question 7 (ii)

Solution. Three directions are involved — field, current and force — and when the current is at right angles to the field, the force is at right angles to both. Fleming’s left-hand rule matches each of them to a finger of the left hand, held so that the thumb, first finger and second finger are at right angles to one another:

If the first finger points along the magnetic field and the second finger along the current, the thumb points in the direction of the force on the conductor, which is the way it moves.

Question 7 (iii)

Solution. When a coil turns in a magnetic field, a current is produced (induced) in it; this is how an electric generator works. The direction of this induced current is given by Fleming’s right-hand rule. Stretch the thumb, first finger and second finger of your right hand so that they are at right angles to one another. If the first finger points along the magnetic field and the thumb along the direction in which the conductor moves, the second finger points in the direction of the induced current. An easy way to keep the two Fleming rules apart: the left hand is for motors (a current makes something move), the right hand is for generators (movement makes a current).

Note on the book. The present edition of the chapter no longer includes the section on electromagnetic induction and the electric generator, and Fleming’s right-hand rule does not appear in it. That is why the answer key gives answers to parts (i) and (ii) only. Part (iii) is left over from that section; the rule it asks for is the one above.

Question 8

When does an electric short circuit occur?

Solution. Normally the current flows from the live wire, through the appliance, and back along the neutral wire, and the resistance of the appliance keeps the current to a safe size. If the insulation of the wires is damaged, or there is a fault inside the appliance, the live wire and the neutral wire can come into direct contact. The current then flows straight from one to the other without passing through the appliance, so there is almost no resistance in its path and, by $I = V/R$, the current rises abruptly to a very large value. This is a short circuit. The chapter treats it as one way a circuit can be overloaded; connecting too many appliances to one socket also draws too much current, but that is overloading, not a short circuit.

Question 9

What is the function of an earth wire? Why is it necessary to earth metallic appliances?

Solution. The earth wire, with green insulation, is connected to a metal plate buried deep in the ground near the house. The metal body of an appliance is joined to this wire, which gives any current a path to the earth that has very low resistance.

Metallic appliances need it because metal conducts. Suppose the insulation of the live wire inside an electric iron wears through and the live wire touches the iron’s metal body. Without an earth wire, the whole body would be at the potential of the live wire, and anyone who touched it would give the current a path through their body to the ground — a severe electric shock. With the body earthed, the leaking current flows away through the low-resistance earth wire instead, and the body stays at the potential of the earth, so touching it is safe. Because the path to earth has so little resistance, the current through it is large, which also blows the fuse and disconnects the faulty appliance.

Common mistakes

• Question 1: choosing radial lines, option (c). The field of a wire is pictured as spreading out from it, like light from a lamp. But the iron filings in Activity 12.5 form circles round the wire, and a compass needle placed near the wire turns so that it lies along those circles, never pointing straight at the wire.
• Question 2: choosing “reduces substantially”. The word “short” suggests that something has been cut off. What has actually been cut out is the resistance of the appliance, and with less resistance, $I = V/R$ becomes larger, not smaller.
• Question 3(a): marking it false because “the field of a current is always circles”. That is true close to a single straight wire. Inside a coil the fields of all the turns add up in the same direction, and the result is parallel straight lines — the uniform field of Fig. 12.10.
• Question 5: saying the force is largest when the conductor lies along the field. It is the other way round: when the current is along the field lines there is no force at all, and the force is largest when the current is at right angles to the field.
• Question 6: answering “vertically upwards”. This comes from putting the second finger along the electron beam. Fleming’s rule uses the conventional current, which flows opposite to the electrons, so here it points back towards you, and the field comes out as downwards.
• Question 6 and Question 7: using the wrong hand. The right-hand thumb rule gives the field round a current; Fleming’s left-hand rule gives the force on a current; Fleming’s right-hand rule gives an induced current. Using the right hand for a force question reverses the answer.
• Question 8: confusing a short circuit with overloading. Both make the current too large, but for different reasons. A short circuit is the live and neutral wires touching, so the current skips the appliance; overloading from too many appliances on one socket is a different fault.
• Question 9: thinking the earth wire carries the current all the time. That is the job of the live and neutral wires. The earth wire carries a current only when something goes wrong and current leaks to the metal body.

Practise next

• The in-text questions of this chapter, thirteen across five boxes, which follow the argument exactly: that a magnet has a field, what its field lines mean, the field a current makes, the force a field puts on a current, and the safety of the mains circuit.
• Chapter 11, Electricity — Ohm’s law, the heating effect of a current and the working of a fuse, which lie behind Questions 2, 8 and 9 here.