4.3 Force on a Current-Carrying Conductor and Domestic Circuits
A magnetic field pushes on a wire that carries a current โ the push that spins every electric motor โ and Fleming's left-hand rule tells you which way. The same current, wired into a house through live, neutral and earth wires, fuses and MCBs, must be made safe.
Take a short aluminium rod, lay it across two metal rails between the poles of a strong magnet, and connect the rails to a battery. The moment the key is pressed, the rod rolls along the rails as if an invisible hand had shoved it. Reverse the battery and it rolls the other way; turn the magnet upside down and it reverses again. Nobody touched the rod: the push came from the magnetic field acting on the current in it.
This push is the heart of the electric fan, the washing machine, the mixer-grinder and the loudspeaker. In the first half of this section you will learn what the force depends on and find its direction with Fleming's left-hand rule. In the second half you turn to the wiring of a house โ the live, neutral and earth wires, and the fuse and MCB that stand guard against overloading and short-circuiting โ using the heating effect and power you met in Chapter 3. Along the way you will see why the mains is alternating current (AC) and what its advantage over direct current (DC) is. (How the push spins an electric motor, and how switching the idea round โ a moving wire producing a current โ gives electromagnetic induction and the generator, is in the ๐ school-assessment box in the middle of this section.)
The Force on a Current-Carrying Conductor
In Section 4.2 a current produced a magnetic field that turned a compass needle: the wire pushed on the magnet. By Newton's third law the magnet must push back on the wire with an equal and opposite force. A French physicist, Andrรฉ-Marie Ampรจre, suggested this soon after รrsted's discovery, and it is easy to test. Hang a straight aluminium rod AB from two light wires so that it lies across the gap of a horseshoe magnet, with the magnet's field pointing vertically through it. Connect the ends of the rod, through a key, a rheostat and a battery, to make a circuit. When a current flows the rod is displaced โ it swings out of the gap in one direction. A magnet has no effect on a rod that carries no current, and aluminium is not magnetic, so the force must be on the current.
When a conductor that carries an electric current is placed in a magnetic field, the field exerts a force on the conductor. It is called the magnetic force on the conductor, and it acts on a conductor only while a current flows in it.
Repeat the experiment while changing one thing at a time and you find the pattern summed up below. Increase the current with the rheostat and the rod swings further; use a stronger magnet and it swings further; use a longer rod, so that more of the conductor lies in the field, and again the push is bigger. Now rotate the magnet so that the field points along the rod instead of across it โ and the rod does not move at all.
- Size. The force is directly proportional to the current $I$, to the strength of the field $B$, and to the length $l$ of conductor that lies in the field: $F\propto B\,I\,l$ (when the conductor is at right angles to the field). Double the current and the force doubles.
- Orientation. The force is greatest when the current is at right angles to the field, and zero when the conductor lies parallel to the field. At angles in between it is somewhere between the two.
- Direction. The force is at right angles to both the field and the current โ it points in neither of those two directions.
- Reversal. Reversing the current or reversing the field reverses the force. Reversing both leaves the force as it was.
Fleming's Left-Hand Rule
Because the force is at right angles to both the field and the current, you need three mutually perpendicular directions. Anyone can set them up with the left hand: stretch the thumb, the forefinger and the middle finger of your left hand so that they are at right angles to one another, like the three edges of a box meeting at a corner. John Ambrose Fleming of London turned this into a rule that is easy to remember.
Stretch the thumb, forefinger and middle finger of the left hand so that they are mutually perpendicular. If the forefinger points in the direction of the magnetic field and the middle finger points in the direction of the current, then the thumb points in the direction of the force on the conductor (the direction in which it tends to move).
Memory aid: "First finger = Field, seCond finger = Current, Thumb = Thrust" (thrust means force and motion). The current direction is always the conventional one, from the $+$ terminal to the $-$ terminal outside the cell.
The rule needs the current to be perpendicular to the field. If it is not, use only the part of the picture that is โ and if the wire lies along the field there is no force and nothing to find.
The electric motor, electromagnetic induction (with Fleming's right-hand rule) and the AC and DC generator are in the CBSE 2026-27 syllabus for this chapter, but they are taught and tested in school only โ not in the year-end board exam. Induction and the AC generator come back, with numbers, in Class 12 Physics, where they are also in the JEE Main and NEET syllabi.
The electric motor. Place a rectangular coil ABCD of insulated copper wire between the poles of a magnet so that it can turn about an axis through its middle, with its sides AB and CD at right angles to the field. Pass a current through it. The current flows one way along AB and the opposite way along CD, so by Fleming's left-hand rule one side is pushed up and the other down: the coil turns. After half a turn AB and CD have changed places, and if the current kept its direction the forces would now turn the coil back. A split-ring commutator prevents this: the ends of the coil are joined to the two halves of a split metal ring, which press against two fixed carbon brushes joined to the battery. Every half turn the halves swap brushes, so the current in the coil reverses exactly when it must, and the coil keeps turning the same way. Real motors use a coil of many turns wound on a soft-iron core (together called the armature), and often an electromagnet in place of the permanent magnet, to make the turning effect larger.
Electromagnetic induction. In 1831 Michael Faraday discovered the reverse of the motor effect. Join a coil to a galvanometer (a sensitive current meter whose needle can swing either way from zero) and push the N-pole of a bar magnet into the coil: the needle kicks one way. Hold the magnet still inside the coil: no deflection. Pull it out: the needle kicks the other way. Moving the coil instead of the magnet works just as well, and so does switching the current on or off in a second coil placed nearby. A changing magnetic field through a coil, or a conductor moving across a field, produces a current; this is electromagnetic induction, and the current is the induced current. It is larger when the motion is faster, the magnet is stronger or the coil has more turns.
Fleming's right-hand rule. Stretch the thumb, forefinger and middle finger of the right hand so that they are mutually perpendicular. If the forefinger points along the magnetic field and the thumb along the motion of the conductor, the middle finger points along the induced current. (Left hand: a current makes a motion โ motors. Right hand: a motion makes a current โ generators.)
The electric generator. Turn the coil by an outside force โ a turbine, an engine or a hand crank โ instead of feeding it a current, and its sides cut across the field: a current is induced. Each side moves up through the field for half a turn and down for the next half, so the current in the coil reverses every half turn. If the ends of the coil go to two separate full rings (slip rings), the outer circuit receives this reversing current: an AC generator. If they go to a split-ring commutator, the connections swap every half turn just as the coil's current reverses, so the current in the outer circuit always flows the same way: a DC generator. A coil turning $50$ times a second gives $50\ \text{Hz}$ AC, whose current changes direction twice per turn โ $100$ times a second.
Domestic Electric Circuits
Electricity reaches your home from the nearest transformer through a cable with two wires: the live wire and the neutral wire. In India the potential difference between them is $220\ \text{V}$. The neutral wire is connected to the ground at the power station and is at (almost) the same potential as the Earth; the live wire is at $220\ \text{V}$ relative to the Earth, which is why touching it is dangerous. (The supply is alternating, as explained just below; for the safety ideas of this section the direction of the current does not matter.) Inside the house, a third wire joins them, running to a metal plate buried deep in the ground near the building: the earth wire.
The live wire brings the current into the house at $220\ \text{V}$ above the Earth. The neutral wire takes it back to the supply at (nearly) the potential of the Earth. The earth wire is a safety wire joined to a metal plate deep in the ground; it normally carries no current and is connected to the metal bodies of appliances.
| Wire | Insulation colour (traditional) | Newer wiring | Potential | Job |
|---|---|---|---|---|
| live | red | brown | $220\ \text{V}$ above Earth | carries current to the appliance |
| neutral | black | blue | about $0\ \text{V}$ | carries current back |
| earth | green | greenโyellow | $0\ \text{V}$ | safety path to the ground |
AC and DC. A cell or a battery gives direct current (DC): it always flows the same way round the circuit. The mains gives alternating current (AC): its direction reverses again and again. In India the mains frequency is $50\ \text{Hz}$ โ $50$ complete cycles every second. In each cycle the current flows one way and then the other, so it changes direction twice per cycle: the mains current reverses $100$ times every second, once every $\tfrac{1}{100}\ \text{s}=0.01\ \text{s}$. A lamp or a heater works equally well on either, because the heating effect does not depend on the direction of the current.
Why do power stations send out AC rather than DC? The advantage of AC over DC is that electric power can be transmitted over long distances without much loss of energy. The voltage of AC can be raised and lowered easily (with devices called transformers, studied in Class 12 Physics), so electricity crosses the country at a very high voltage and a small current โ little energy is wasted as heat $I^2Rt$ in the long cables โ and is brought down to a safe $220\ \text{V}$ near your home. DC cannot be stepped up and down so simply.
Inside the house, the supply passes first through the main fuse (or main MCB), the energy meter and the main switch, and then divides into separate circuits. Typically one circuit with thin wires and a $5\ \text{A}$ rating serves the lights, fans and other low-power appliances; another with thicker wires and a $15\ \text{A}$ rating serves the power sockets for heavy appliances such as the geyser, air conditioner, refrigerator and room heater. Within each circuit the appliances are joined in parallel between the live and neutral wires, for two reasons you already know from Section 3.3: each gets the full $220\ \text{V}$, and each can be switched on and off independently of the others.
- Appliances are connected in parallel across the live and neutral wires, so each has $220\ \text{V}$ and works independently.
- The switch and the fuse or MCB are placed in the live wire, so that when they are open the appliance is cut off from the $220\ \text{V}$ completely. (A fuse in the neutral would leave the appliance connected to the live wire even when it has blown.)
- A three-pin plug has a live pin, a neutral pin and a thicker, longer earth pin that connects the metal body of the appliance (an iron, a geyser, a refrigerator) to the earth wire.
- Earthing is the safety purpose of the earth wire: if the live wire accidentally touches the metal body, a large current flows through the low-resistance earth wire into the ground, the fuse blows or the MCB trips at once, and the body never stays at $220\ \text{V}$. Without earthing, the body becomes live and anyone touching it provides the path to the ground โ an electric shock.
Overloading, Short-Circuiting and Safety Devices
A wire that carries too much current gets hot, because the heat produced is $H=I^2Rt$. Two different faults cause the current to become too large. The first you already know from Section 3.4: overloading โ switching on so many appliances on one circuit that the total current exceeds what the wires are made to carry. The second is much more violent.
A short circuit happens when the live and neutral wires touch each other directly (for example when the insulation of a worn wire fails), so that the current bypasses the appliance. The resistance of the path then becomes very small and, from $I=\dfrac VR$, the current becomes very large โ hundreds or thousands of amperes โ in a fraction of a second. The wires overheat, spark, and may start a fire.
Because current in all the appliances adds up in the live wire (Section 3.3), a protective device is placed in the live wire at the start of every circuit. The old device is the fuse (Section 3.4): a thin wire that melts and must be replaced. Most modern homes use the second device.
An MCB is an automatic switch connected in series in the live wire. It trips โ opens the circuit โ when the current exceeds its rating (for example $15\ \text{A}$). In many MCBs the current passes through a small electromagnet (Section 4.2): a sudden huge current, as in a short circuit, makes the electromagnet pull a lever and open the contacts at once, while a slow overload heats a bimetallic strip that bends and does the same. After the fault is cleared the MCB is simply switched back on โ no part has to be replaced.
| Fuse | MCB | |
|---|---|---|
| How it works | wire melts when $I$ is too large | electromagnet / heated strip opens a switch |
| After a fault | wire must be replaced | switched back on |
| Speed | slower, depends on the wire | fast, accurate rating |
| Safety | can be wrongly replaced by thick wire | cannot be defeated that way |
- The current taken by an appliance on the mains is $I=\dfrac PV$, with $V=220\ \text{V}$. The currents of appliances in parallel add; the total must stay below the rating of the circuit's fuse or MCB.
- A fuse or MCB is rated a little above the normal current of the circuit it guards. It must never be replaced by a thicker wire or a higher rating than the wires can carry.
- Overloading (too many appliances), short-circuiting (live touches neutral) and a live-to-body fault (live touches a metal casing โ dealt with by earthing) are the three faults; each makes the fuse blow or the MCB trip.
1. Wrong hand. Fleming's rule for the force on a wire uses the left hand. The thumb rule of Section 4.2, which gives the field made by a current, uses the right hand. The thumb means "current" in one and "force" in the other โ decide which question you are asking.
2. Fingers not at right angles. The three fingers must be mutually perpendicular. If the current is parallel to the field there is no force and nothing to find; do not squeeze the fingers together to "get an answer".
3. Force along the field. The force is never along the field or along the current. It is at right angles to both.
4. Current direction. Use the conventional direction, from $+$ to $-$ outside the cell; a student who follows the electrons gets every force backwards.
5. Fuse or switch in the neutral wire. Both belong in the live wire, so that an appliance that is "off" is genuinely cut off from the $220\ \text{V}$.
6. Thick wire in place of a fuse. A fuse that is stronger than the wiring protects nothing: the cable burns before the fuse melts.
7. "The earth wire carries the current to the appliance." It carries current only during a fault. In normal working it is idle, and the appliance works equally well without it โ which is exactly why people dangerously remove it.
In JEE Main, NEET and JEE Advanced 2026; not in the CBSE Class 10 syllabus.
For a straight conductor of length $l$ carrying a current $I$ in a uniform field $B$, making an angle $\theta$ with the field,
$$F=B\,I\,l\,\sin\theta$$with $B$ measured in tesla ($1\ \text{T}=1\ \text{N A}^{-1}\text{m}^{-1}$). It is greatest, $F=BIl$, at $\theta=90^\circ$ and zero at $\theta=0^\circ$ โ the rule of Result 4.7 in numbers. For $B=0.50\ \text{T}$, $I=4.0\ \text{A}$ and $l=0.20\ \text{m}$: $F=0.50\times4.0\times0.20=0.40\ \text{N}$ at $90^\circ$, and $0.40\times\sin30^\circ=0.20\ \text{N}$ if the rod makes $30^\circ$ with the field. The direction is that given by Fleming's left-hand rule using the component of the current at right angles to the field. You will meet this force in Class 12 Physics, Moving Charges and Magnetism, together with the force on a moving charge.
Exercises
- 1 When does a conductor placed in a magnetic field experience a force?
- 2 Name three quantities that decide the size of the force on a conductor at right angles to a magnetic field.
- 3 How must a straight conductor be placed in a magnetic field for the force on it to be (a) greatest, (b) zero?
- 4 A rod at right angles to a field carries $2.0\ \text{A}$ and feels a force of $0.30\ \text{N}$. What is the force when the current is $6.0\ \text{A}$?
- 5 A conductor feels a force of $0.45\ \text{N}$. The magnet is replaced by one with a field three times weaker, and the current is doubled. What is the force now?
- 6 Why does an aluminium rod, which is not magnetic, move when a current flows through it in a magnetic field?
- 7 A current-carrying rod is pushed by a horseshoe magnet. Is the magnet pushed too? Explain.
- 8 The current in a rod is reversed and the magnet is turned over. What happens to the force on the rod?
- 1 State Fleming's left-hand rule. Which finger stands for the field?
- 2 A wire carries a current towards the north in a field pointing vertically downwards. Which way does the force act?
- 3 A current flows eastwards in a field pointing vertically upwards. Find the direction of the force.
- 4 A current flows into the page in a field pointing to the right. Which way is the force: up, down, left or right?
- 5 A current flows out of the page in a field pointing to the right. Which way is the force?
- 6 A vertical field pointing down pushes a wire towards the east. In which direction does the current flow?
- 7 A current flowing east experiences an upward force. In which horizontal direction does the field point?
- 8 Why must the three fingers be at right angles, and what does it tell you about the direction of the force?
- 1 Name the three wires of a domestic circuit, give the traditional colour of each, and state which one is at $220\ \text{V}$ above the Earth.
- 2 Why are the switch and the fuse always connected in the live wire?
- 3 What is the purpose of the earth wire? Why is the metal body of a geyser earthed?
- 4 The earth pin of a three-pin plug is thicker and longer than the other two. Give a reason.
- 5 Why are household appliances connected in parallel and not in series?
- 6 Name two causes of too large a current in a household circuit. Which device protects the wiring?
- 7 What is the current taken by a $1.1\ \text{kW}$ iron from the $220\ \text{V}$ mains?
- 8 How many $60\ \text{W}$ bulbs can be run on a $5\ \text{A}$ lighting circuit at $220\ \text{V}$ without blowing the fuse?
- 9 Which of $3\ \text{A}$, $5\ \text{A}$ and $10\ \text{A}$ is the right fuse for a $1.5\ \text{kW}$ room heater at $220\ \text{V}$?
- 10 What is the difference between direct and alternating current? State one advantage of AC over DC, and say how many times a second the current of the $50\ \text{Hz}$ mains changes direction.
- 1 A loudspeaker has a coil, glued to its cone, that sits in the field of a permanent magnet. Explain how the music-carrying current makes the cone vibrate.
- 2 Say in one sentence the difference between what the right-hand thumb rule and Fleming's left-hand rule tell you.
- 3 Give two advantages of an MCB over a fuse.
- 4 A kitchen circuit has a $15\ \text{A}$ MCB. A toaster ($0.80\ \text{kW}$), a kettle ($1.8\ \text{kW}$) and a microwave oven ($1.2\ \text{kW}$) work on $220\ \text{V}$. Find the current of each and say which of the three can be used together safely.
- 5 A person replaces a blown fuse by a piece of thick copper wire. Explain what could happen at the next short circuit.
- 6 Challenge. A $2.0\ \text{kW}$ geyser is plugged into a $5\ \text{A}$ lighting circuit by mistake. Find the current, say what happens, and say which circuit it needs.
- 1 What is the job of the split-ring commutator in an electric motor? What would the coil do without it?
- 2 A magnet is pushed into a coil joined to a galvanometer, held still inside it, and then pulled out. Describe the galvanometer reading in each stage.
- 3 State Fleming's right-hand rule. When do you use it instead of the left-hand rule?
- 4 A horizontal wire running northโsouth is moved vertically downwards through a horizontal field that points east. Find the direction of the induced current.
- 5 Name two ways of making the induced current in a coil larger.
- 6 How does an AC generator differ from a DC generator in construction and in what it supplies?
- 7 The coil of a generator turns $25$ times a second with slip rings. Find the frequency of the AC and the number of times a second its current changes direction.
E1. Board ยท 2 marks State Fleming's left-hand rule. A conductor carries a current towards the east in a magnetic field pointing vertically upwards. In which direction is the force on the conductor?
E2. Board ยท 3 marks What is the function of the earth wire in a domestic circuit? What happens when the live wire touches the metal body of an earthed geyser? Name two safety devices used in a house.
E3. Board ยท AssertionโReason Assertion (A): A straight conductor carrying a current parallel to a magnetic field experiences no force. Reason (R): The force on a current-carrying conductor in a magnetic field acts along the direction of the field. (A) Both A and R are true and R explains A. (B) Both are true but R does not explain A. (C) A is true but R is false. (D) A is false but R is true.
E4. Board ยท Case study A kitchen power circuit on $220\ \text{V}$ is protected by a $15\ \text{A}$ MCB. It supplies a toaster ($0.80\ \text{kW}$), a kettle ($1.8\ \text{kW}$) and a microwave oven ($1.2\ \text{kW}$). (i) Find the current drawn by each appliance and the total current when all three are switched on. [2 marks] (ii) Will the MCB trip? Give a reason. [1 mark] (iii) Which wire connects the metal casing of the kettle to the ground, and why is it needed? [1 mark]
E5. NEET A straight wire at right angles to a uniform magnetic field experiences a force $F$. The current is tripled and the magnet is replaced by one whose field is one-third as strong. The force is now (A) $9F$ (B) $F$ (C) $3F$ (D) $\dfrac F9$
E6. JEE Main A vertical wire carries a current downwards in a uniform horizontal magnetic field that points north. The force on the wire points (A) east (B) west (C) north (D) vertically upwards
Research question. How close to its limit does an ordinary home run its circuits โ and which combinations of everyday appliances would trip the MCB?
Why it matters. Electrical fires in homes are very often caused by overloaded extension boards and wrong-rated fuses. Engineers decide how thick the wires must be and what rating the MCB should have by estimating the largest current a household could draw. Cities plan their supply networks the same way: they ask how often many homes switch on a geyser, a cooler and a heater at the same time.
What to do.
- With an adult, read โ without opening anything โ the ratings printed on the MCBs in your home's distribution board (for example $5\ \text{A}$, $15\ \text{A}$), and note which room or appliance each protects.
- List every appliance in the home with its power rating from the label (W or kW). Compute each one's current from $I=\dfrac PV$ with $V=220\ \text{V}$ (or your local voltage).
- For each circuit, find the combination of appliances that could be on together, add the currents, and compare the total with the MCB rating. Which circuit has the smallest margin?
- Propose one rule for the household ("never run the geyser and the heater together") and justify it with your numbers.
Tools: a notebook, a phone camera for labels, a calculator or spreadsheet; optionally a clamp meter used by an electrician on a sample appliance.
Hand in: A table of appliances, ratings and currents, a comparison with each MCB rating, and a short written rule with your reasoning.
Going further. The plug of a UK appliance has its own small fuse, and North American homes run at $120\ \text{V}$ โ a $1.5\ \text{kW}$ heater there needs about $12.5\ \text{A}$ instead of $6.8\ \text{A}$. What does that say about the thickness of wire needed at the lower voltage for the same power?
๐งช Self-check quiz
Q1. A straight wire carrying a current experiences no magnetic force when it is
Q2. In Fleming's left-hand rule, the thumb gives the direction of
Q3. The fuse or MCB of a domestic circuit is connected in
Q4. A very large current flows when the live and neutral wires touch each other. This is called
Q5. A rod in a field feels a force $F$. The current is doubled and the field is also doubled. The force becomes