Magnetic field & field lines
A fridge magnet sticks to the door without any glue, and a compass in your hand always settles pointing north. Both show an invisible push or pull that spreads around a magnet.
A magnet has two poles, north and south. Like poles repel and unlike poles attract. The magnetic field is the region around a magnet in which its force can be felt; it has both size and direction. The field is drawn with field lines: outside the magnet they run from the north pole to the south pole, and inside from south to north, so they form closed curves. Lines that are crowded show a stronger field (near the poles), and two lines never cross. A compass needle is a small magnet that turns along the field; its north pole shows the direction of the field.
Equation / formula : Outside a magnet: N → S · Inside: S → N · crowded lines = strong field · lines never cross · like poles repel, unlike poles attract
In the figure : Field lines leave the north pole, enter the south pole and are closest together near the poles.
Rule 1 : Poles: attract or repel — Unlike poles (N–S) pull towards each other; like poles (N–N or S–S) push apart. A compass needle turns so that its north pole points the way the field points.
- Easy : Two magnets are held with north poles facing: they push apart.
- Medium : A compass is placed next to the south pole of a bar magnet. Its north end points towards the magnet, because unlike poles attract.
- For exams : A suspended magnet repels the north end of a compass needle. That end of the magnet is a north pole, since only like poles repel.
Rule 2 : Reading field lines — Look at how close the lines are to judge strength, and at the arrows to find direction. Crowded lines mean a strong field; widely spaced lines mean a weak one. Equal, parallel lines mean a uniform field.
- Easy : Lines 2 mm apart at P and 6 mm apart at Q: the field is stronger at P.
- Medium : A small north pole is moved from crowded lines to widely spaced lines. The force on it decreases.
- For exams : A student says two field lines cross near the pole. That is impossible, because at a crossing point a compass would have to point in two directions at once.
Field lines are imaginary. They are only a way to picture the field; iron filings make the pattern visible.
Saying that field lines stop at the poles. They carry on inside the magnet from south to north and form closed loops.
Out of N, into S, closed loops, never crossing. Memory clue : "Out of North, into South" (ONIS): lines leave the north pole and enter the south pole outside the magnet.
Spot the difference
| Point | Strong field | Weak field |
|---|---|---|
| Field lines | crowded, close together | widely spaced |
| Where found | near the poles | far from the magnet |
Practice questions
- 1What do we call the region around a magnet where its force can be felt?
- 2In which direction do field lines run outside a bar magnet?
- 3What does the closeness of field lines tell us?
- 4Why can two field lines never cross?
- 5Lines are 3 mm apart near pole A and 9 mm apart near the side of the magnet. Where is the field stronger?
- 6A compass needle is brought near the south pole of a magnet. Which end of the needle points to the magnet?
- 7What shape of field lines show a uniform field?
- 8Which two organs of the human body produce a magnetic field that is large enough to be useful in MRI?
Show answers (try them yourself first)
- 1The magnetic field.
- 2From the north pole to the south pole (and from south to north inside).
- 3The strength of the field: crowded lines mean a strong field.
- 4Because at the crossing point the field would have two directions at once.
- 5Near pole A, because the lines are closer.
- 6Its north end, because unlike poles attract.
- 7Equally spaced parallel straight lines.
- 8The heart and the brain.
Magnetic field due to a straight current-carrying wire
Flip a switch and a compass lying beside the wire jerks sideways. Nothing touches the needle; the current in the wire creates a magnetic field around it.
In 1820 Hans Christian Oersted noticed that a current-carrying wire deflects a nearby compass needle, which showed that electricity and magnetism are linked. Around a long straight wire the field lines are concentric circles in a plane perpendicular to the wire. Their direction comes from the right-hand thumb rule: hold the wire in your right hand with the thumb along the current, and the curled fingers show the direction of the field (Maxwell’s corkscrew rule says the same). Reversing the current reverses the field. The field grows with the current and weakens as you move away from the wire.
Equation / formula : Thumb = current · curled fingers = field · field grows with I · field falls as distance grows (B ∝ I/d)
In the figure : The field of a straight wire is a set of circles; use the right hand, thumb along the current.
Rule 1 : Direction of the field — Point the right thumb along the current and curl the fingers. Current towards you gives anticlockwise circles; current away from you gives clockwise circles.
- Easy : A vertical wire carries current upwards: seen from above, the field circles run anticlockwise.
- Medium : A horizontal wire carries current towards the east. Directly above the wire the field points south; directly below it points north.
- For exams : Two compasses sit on opposite sides of a vertical wire at equal distances. Their needles deflect in opposite directions, because the field direction is opposite on opposite sides.
Rule 2 : Strength of the field — The field at a point is directly proportional to the current and gets weaker with distance from the wire. Doubling the current doubles the field; tripling the distance makes it one-third.
- Easy : Current rises from 2 A to 6 A at the same point: the field becomes 3 times as strong.
- Medium : A compass 2 cm from a wire deflects more than one 6 cm away, because the field is weaker farther from the wire.
- For exams : The field is B at 3 cm and the current stays the same. At 9 cm the field is B ÷ 3, so it is less than B. Changing the colour of the insulation changes nothing.
With no current there is no field from the wire: switch off and the compass returns to its north-south position.
Using the left hand for the thumb rule. For the field of a wire, use the right hand; the left hand is for the force rule.
Thumb for current, fingers for field, right hand. Memory clue : "Thumb Takes the Current" (right hand): thumb = current, curl = field.
Spot the difference
| Point | Straight wire | Bar magnet |
|---|---|---|
| Field lines | concentric circles around the wire | closed curves from N to S outside |
| Direction rule | right-hand thumb rule | compass: north pole shows it |
Practice questions
- 1Who discovered that a current-carrying wire deflects a compass needle?
- 2What is the shape of the field lines around a long straight wire?
- 3State the right-hand thumb rule.
- 4What happens to the compass deflection when the current is reversed?
- 5A current of 1.5 A is raised to 4.5 A. By what factor does the field at a fixed point change?
- 6A vertical wire carries current downwards. Seen from above, are the field circles clockwise or anticlockwise?
- 7Current flows towards the north in a horizontal wire. In which direction is the field directly above the wire?
- 8Does the field at a point depend on the colour of the wire’s insulation?
Show answers (try them yourself first)
- 1Hans Christian Oersted.
- 2Concentric circles centred on the wire.
- 3Hold the wire in the right hand with the thumb along the current; the curled fingers give the field direction.
- 4The deflection reverses.
- 54.5 ÷ 1.5 = 3, so the field becomes 3 times as strong.
- 6Clockwise.
- 7Towards the east.
- 8No. It depends on the current and the distance only.
Circular loop, solenoid & electromagnet
A scrapyard crane lifts a wrecked car with a big disc, then lets it drop the instant the operator flips a switch. The disc is an electromagnet: it is a magnet only while current flows.
Every small piece of a current-carrying circular loop gives circular field lines, and near the centre of the loop they look like straight lines, perpendicular to the plane of the loop. A coil of n turns gives n times the field because all turns add up. A solenoid is a long coil of many close circular turns; its field is like that of a bar magnet, uniform inside and parallel to the axis, with one end a north pole and the other a south pole. To find the poles, view an end: anticlockwise current gives a north pole, clockwise current gives a south pole. A piece of soft iron inside the solenoid becomes a strong magnet, called an electromagnet. It can be switched off, and its strength can be changed with the current and the number of turns.
Equation / formula : Field ∝ number of turns · field ∝ current · anticlockwise end = N · clockwise end = S · soft iron core makes an electromagnet
In the figure : More turns, more current and a soft iron core all make the electromagnet stronger.
Circular loop, solenoid & electromagnet
In the app you can move this figure with your finger.
Open in the appRule 1 : Strength of a coil or solenoid — The field at the centre grows with the number of turns and with the current, and falls if the loop is made bigger. Double the turns or double the current and the field doubles.
- Easy : A coil of 25 turns carries 2 A; a coil of 50 turns of the same size also carries 2 A: the field is twice as strong.
- Medium : A 40-turn coil gives about 40 times the field of a single loop with the same current, since all 40 fields add up.
- For exams : A coil of 100 turns carries 3 A. If the current is made 1.5 A and the turns 200, the field stays the same: the current is halved but the turns are doubled.
Rule 2 : Poles of a coil and uses of electromagnets — Look at one end of the coil. Anticlockwise current makes that end a north pole; clockwise makes it a south pole. Reversing the cell swaps the poles. Electromagnets are used in cranes, electric bells and for removing iron splinters.
- Easy : Looking at one end of a solenoid, the current is clockwise: that end is a south pole.
- Medium : A compass north pole is repelled by one end of a solenoid. That end is a north pole, because like poles repel.
- For exams : Steel kept inside a coil stays magnetised after the current stops, so it makes a permanent magnet; soft iron loses its magnetism quickly, so it suits an electromagnet.
Inside a long solenoid the field is uniform, so the lines are parallel and equally spaced; outside it is weak.
Using steel for the core of an electromagnet. Steel keeps its magnetism, so the load would not drop when the current is switched off. Use soft iron.
Anticlockwise = North, clockwise = South; soft iron core, more turns, more current. Memory clue : "ANC": Anticlockwise = North, Clockwise = South. For an electromagnet, think "Soft iron, Switch off".
Spot the difference
| Point | Electromagnet | Permanent magnet |
|---|---|---|
| Made of | soft iron core in a coil | steel |
| Strength and switching | can be changed or switched off | fixed, cannot be switched off |
Practice questions
- 1What is a solenoid?
- 2How is the field inside a long solenoid?
- 3Looking at one end of a solenoid, the current is anticlockwise. Which pole is that end?
- 4Why is soft iron used as the core of an electromagnet?
- 5Name two ways of making an electromagnet stronger.
- 6A 60-turn coil is replaced by a 180-turn coil of the same size with the same current. How does the central field change?
- 7The cell of a solenoid is reversed. What happens to its poles?
- 8Give two uses of electromagnets.
Show answers (try them yourself first)
- 1A long coil of many close circular turns of insulated wire.
- 2Uniform: parallel straight lines along the axis.
- 3A north pole.
- 4It magnetises easily and loses its magnetism easily.
- 5Increase the current; increase the number of turns.
- 6180 ÷ 60 = 3, so the field becomes 3 times as strong.
- 7The poles interchange.
- 8Lifting iron scrap with a crane; electric bells (also removing iron splinters from the eye).
Force on a current-carrying conductor (Fleming’s left-hand rule)
A ceiling fan, a mixer and a water pump all turn because of one idea: a wire carrying current inside a magnetic field is pushed sideways.
A conductor carrying current in a magnetic field feels a force, because a magnet and a current exert forces on each other (suggested by André-Marie Ampère). The force is greatest when the current is at right angles to the field and zero when it is parallel to the field. Reversing the current or the field reverses the force. Fleming’s left-hand rule gives its direction: stretch the thumb, forefinger and middle finger of the left hand at right angles; if the forefinger shows the field and the middle finger the current, the thumb shows the force. An electric motor uses this force on a coil, and a split-ring commutator reverses the current every half turn so that the coil keeps turning one way. A moving charge, such as an electron beam, feels the same kind of force.
Equation / formula : Force is largest when I ⟂ B and zero when I ∥ B · thumb = Force, forefinger = Field, middle finger = Current · force ∝ current
In the figure : Forefinger for field, middle finger for current, thumb for force, all at right angles and all on the left hand.
Rule 1 : Direction of the force — Use the left hand. Point the forefinger along the field and the middle finger along the current; the thumb gives the force. If either the current or the field is reversed, the force reverses; if both are reversed, it stays the same.
- Easy : Field points up and current flows from south to north: the thumb points east, so the force is towards the east.
- Medium : Field points north and current flows upward: forefinger north, middle finger up, so the thumb points west and the force is towards the west.
- For exams : A proton moves along the direction of the field. No force acts on it, because the force is zero when the motion is parallel to the field.
Rule 2 : Size of the force and the motor — The force grows with the current, the strength of the magnet and the length of wire in the field. A motor turns faster with more turns, a stronger magnet or more current; reversing the battery only reverses the direction of rotation.
- Easy : The force on a wire is 0.3 N at 4 A. At 2 A it is 0.15 N, because force is directly proportional to current.
- Medium : To reverse a motor, reverse the battery. To make it spin faster, add turns, use a stronger magnet or raise the current; reversing the battery alone will not speed it up.
- For exams : Without the commutator the coil would turn half a turn and stop, because the current would not reverse and the forces would then pull it back.
Two long parallel wires carrying current in the same direction attract each other; opposite currents repel.
Using the right hand for the force. The force rule uses the left hand. The right-hand thumb rule is only for the field of a wire.
Left hand, three fingers at right angles: Field – Current – Force. Memory clue : "FBI": Force = thumb, B (field) = forefinger, I (current) = middle finger, all on the left hand.
Spot the difference
| Point | Right-hand thumb rule | Fleming’s left-hand rule |
|---|---|---|
| Finds | field direction due to a current | force on a current in a field |
| Fingers | thumb = current, curl = field | thumb = force, forefinger = field, middle = current |
Practice questions
- 1When is the force on a current-carrying conductor in a field the greatest?
- 2State Fleming’s left-hand rule.
- 3What happens to the force if both the current and the field are reversed?
- 4Current flows towards the east and the field points up. In which direction is the force?
- 5What is the job of the split-ring commutator in a motor?
- 6A wire feels a force of 0.8 N at 5 A. What is the force at 2 A in the same field?
- 7Name the energy change in an electric motor.
- 8Why does no force act on a wire lying along the field?
Show answers (try them yourself first)
- 1When the current is at right angles to the field.
- 2Stretch the left thumb, forefinger and middle finger at right angles: forefinger = field, middle finger = current, thumb = force.
- 3The force stays the same: two reversals cancel.
- 4Towards the south (forefinger up, middle finger east, thumb south).
- 5It reverses the current in the coil every half turn so the coil keeps turning in one direction.
- 6Force ∝ current, so 0.8 × 2 ÷ 5 = 0.32 N.
- 7Electrical energy changes into mechanical energy.
- 8Because the force is zero when the current is parallel to the field.
Domestic electric circuits & safety
When you plug a geyser into the wall, the metal body has a green wire joined to the ground. If a loose wire ever touches the body, the current escapes to the earth instead of shocking you.
Homes in India get alternating current (AC) at about 220 V and 50 Hz, so the direction reverses 100 times a second; a cell gives direct current (DC). There are three wires: the live wire (red) at high potential, the neutral wire (black) at zero potential, and the earth wire (green) joined to a metal plate buried in the ground and to the metal bodies of appliances. Appliances are joined in parallel, so each gets 220 V and works on its own. A fuse is a short wire of low melting point joined in series with the live wire; it melts and breaks the circuit when the current is too high. A short circuit happens when live and neutral touch and the current becomes huge; overloading happens when too many appliances draw current from one circuit. Houses use a 5 A circuit for bulbs and fans and a 15 A circuit for geysers and air conditioners. Many homes now use an MCB instead of a fuse.
Equation / formula : I = P/V · live = red, neutral = black, earth = green · 5 A circuit ≈ 1100 W · 15 A circuit ≈ 3300 W at 220 V
In the figure : A fuse is the weak link: it melts first and breaks the circuit before the appliance is harmed.
Rule 1 : Current drawn and the right fuse — Current drawn = power ÷ voltage, I = P/V. Choose a fuse rating a little above this normal current. A fuse that is too low keeps blowing; one that is too high does not protect.
- Easy : A 2200 W oven on 220 V draws I = 2200 ÷ 220 = 10 A.
- Medium : A 660 W appliance draws 3 A, so a 5 A fuse suits it. A 1 A fuse would blow every time it is switched on.
- For exams : A 3 kW air-cooler and a 400 W fan run on one 15 A, 220 V circuit. Total power 3400 W gives I = 3400 ÷ 220 ≈ 15.5 A, which is above 15 A, so the circuit is overloaded.
Rule 2 : Earth wire, short circuit and overloading — The earth wire gives leakage current a safe low-resistance path to the ground, so the body of a metal appliance never stays at a high potential. A short circuit and overloading both send a very large current, and the fuse or MCB cuts it off.
- Easy : A live wire touches the metal body of an earthed iron: the current flows through the earth wire to the ground, and you stay safe.
- Medium : A switch must be fitted in the live wire. When it is off, the appliance is cut off from the high potential and is not live.
- For exams : Replacing a blown 5 A fuse with a thick copper wire is dangerous: copper has a high melting point, so it will not melt and the circuit loses its protection against excess current.
The earth pin of a three-pin plug is longer and thicker, so the earth connection is made first and broken last.
Putting the switch in the neutral wire, or using a copper wire as a fuse. The switch belongs in the live wire and a fuse wire must melt easily.
Live red, neutral black, earth green; fuse and switch in the live wire. Memory clue : "RBG": Red = live, Black = neutral, Green = earth. Also "Fuse melts, Fuse saves".
Spot the difference
| Point | Short circuit | Overloading |
|---|---|---|
| Cause | live and neutral wires touch | too many appliances on one circuit |
| Result | resistance falls, huge current | total current above the safe limit |
Practice questions
- 1What are the voltage and frequency of the domestic AC supply in India?
- 2Give the colour code of the live, neutral and earth wires.
- 3Why is the earth wire joined to the metal body of an appliance?
- 4On what principle does a fuse work, and in which wire is it fitted?
- 5How much current does a 1100 W iron draw on 220 V?
- 6A 3300 W geyser and a 220 W fan are joined to one 15 A, 220 V circuit. Is it overloaded?
- 7Why are household appliances connected in parallel?
- 8Why must a fuse wire be made of a material of low melting point?
Show answers (try them yourself first)
- 1About 220 V and 50 Hz.
- 2Live: red; neutral: black; earth: green.
- 3So that leakage current flows to the ground and the user does not get a severe shock.
- 4The heating effect of current; it is fitted in series with the live wire.
- 5I = 1100 ÷ 220 = 5 A.
- 6Total 3520 W gives I = 3520 ÷ 220 = 16 A, which is more than 15 A, so yes.
- 7Each gets the full 220 V and works independently of the others.
- 8So that it melts easily and breaks the circuit when the current is too high.