Leaving Certificate Physics
๐งฒ Electricity & Magnetism
Magnets, motors, generators, transformers โ it's all connected! This guide covers everything from F = BIL to Faraday's Law, explained simply with diagrams, memory tricks and worked examples.
๐งฒ Chapter 1: Magnets & Fields
๐ช Chapter 2: Current in a Field
โก Chapter 3: EM Induction
Magnets & Fields
Field lines, poles, Earth's field
Chapter 1
Current & Fields
Right hand grip rule, solenoid
Chapter 1
F = BIL
Force on a current-carrying conductor
Chapter 2
Fleming's Left Hand Rule
FBI rule โ direction of force
Chapter 2
F = Bqv
Force on a moving charge
Chapter 2
Circular Motion
Charged particle in magnetic field
Chapter 2
Magnetic Flux
ฮฆ = BA, the weber
Chapter 3
Faraday's Law
emf = N(ฮฮฆ/ฮt), induced voltage
Chapter 3
Lenz's Law
Direction of induced emf, copper pipe
Chapter 3
Transformers
Vs/Vp = Ns/Np, step-up/down
Chapter 3
All Formulas
Quick reference sheet
Revision
All Definitions
Learn these off for the exam
Revision
๐ก How to use this guide: Work through each section using the sidebar. Each section has simple explanations, memory tricks, key definitions to learn, formulas with examples, and quizzes. The ๐ฏ boxes are exam tips โ don't skip them!
Chapter 1 โ Magnets & Fields
๐งฒ Magnets & Magnetic Fields
Every magnet has two poles and creates an invisible field around it. Here's what you need to know.
The Basics
A magnet has a north pole and a south pole. These always come in pairs โ you can NEVER have a magnet with just one pole.
Like Poles
NโN or SโS
REPEL each other โ they push away
Unlike Poles
NโS
ATTRACT each other โ they pull together
๐ Definition โ Magnetic Field
A magnetic field is any region of space where magnetic forces can be felt.
๐บ๏ธ Magnetic Field Lines
We draw field lines to show where the field exists and its direction. The rules for drawing them:
- Field lines go from the North pole to the South pole (outside the magnet)
- Lines that are closer together = stronger field
- Field lines never cross each other
- Between the poles of a U-shaped magnet the field lines are straight and parallel โ uniform field
Field lines run from North to South outside the magnet. Closer lines = stronger field.
๐ The Earth's Magnetic Field
The Earth itself acts like a giant bar magnet! The geographic North Pole is actually a magnetic South Pole โ that's why a compass needle (a north pole) is attracted to it.
Navigation
Compasses and animals (birds, dolphins) use Earth's field to navigate
Protection
Earth's magnetic field deflects dangerous cosmic radiation from the Sun (solar wind)
๐งฒ To Plot a Magnetic Field
๐ฏ Experiment: Plotting magnetic field lines
Place a bar magnet on paper. Place a plotting compass near the magnet. Mark the direction the needle points. Move the compass to the tip of the arrow and repeat. Connect the dots to get a field line. Alternatively, sprinkle iron filings on paper over the magnet โ they align with the field lines.
Place a bar magnet on paper. Place a plotting compass near the magnet. Mark the direction the needle points. Move the compass to the tip of the arrow and repeat. Connect the dots to get a field line. Alternatively, sprinkle iron filings on paper over the magnet โ they align with the field lines.
Chapter 1 โ Magnets & Fields
โก Current Creates a Magnetic Field
Hans Oersted discovered in 1820 that electricity and magnetism are connected โ a wire carrying current creates a magnetic field around it!
Three Types of Field Patterns
Straight Wire
Circular field
Circles of field lines around the wire, like rings around a finger
Loop of Wire
Bar-magnet-like
A single loop creates a field similar to a thin bar magnet
Solenoid
Bar magnet!
Many loops together โ exactly like a bar magnet with N and S poles
โ Right Hand Grip Rule โ Straight Wire
๐ง The Right Hand Grip Rule:
Grip the wire in your RIGHT hand with your THUMB pointing in the direction the current flows.
Your FINGERS curl around the wire in the direction of the magnetic field lines.
Grip the wire in your RIGHT hand with your THUMB pointing in the direction the current flows.
Your FINGERS curl around the wire in the direction of the magnetic field lines.
Current going DOWN the wire โ field lines circle clockwise when viewed from above
๐ Direction in a Solenoid โ CIS Rule
๐ง CIS = Clockwise Is South
Look into the end of a solenoid. If current flows Clockwise โ that end is a South pole.
If current flows anti-clockwise โ that end is a North pole.
Think of it like an "S" and "N" โ the clockwise swirl looks like the bottom of an S when drawn.
Look into the end of a solenoid. If current flows Clockwise โ that end is a South pole.
If current flows anti-clockwise โ that end is a North pole.
Think of it like an "S" and "N" โ the clockwise swirl looks like the bottom of an S when drawn.
๐ฌ Demonstrating the Magnetic Field of a Solenoid
๐ฏ Experiment:
Connect each end of a solenoid (long coil of wire) to a DC power supply. Sprinkle iron filings on paper placed near the solenoid, or use a compass. The pattern that forms is identical to that of a bar magnet โ with a clear north and south pole at each end.
Connect each end of a solenoid (long coil of wire) to a DC power supply. Sprinkle iron filings on paper placed near the solenoid, or use a compass. The pattern that forms is identical to that of a bar magnet โ with a clear north and south pole at each end.
Chapter 1 โ Magnets & Fields
๐ Electromagnets & Their Uses
An electromagnet is a solenoid with an iron core inside. When you turn on the current, it becomes a powerful magnet. Turn it off โ no magnet!
An electromagnet = solenoid (coil of wire) + soft iron core inside. The iron core massively strengthens the magnetic field.
Big advantage over permanent magnets
It can be switched ON and OFF. Change the current โ change the strength. Reverse the current โ reverse the poles!
Why "soft" iron?
Soft iron is easy to magnetise AND de-magnetise. It only acts as a magnet when current flows. Hard iron (steel) would stay magnetised after you turn off the current.
๐ญ Uses of Electromagnets
- Scrapyard cranes โ lift and drop cars (turn off current โ car drops)
- Electric motors โ electromagnets push and pull to create rotation
- Loudspeakers โ electromagnet vibrates a cone to create sound
- Doorbells / electromagnetic relays โ a small current activates a large switch
- MRI scanners โ powerful electromagnets in hospitals
- Maglev trains โ electromagnets underneath the train repel magnetic track โ floats!
Chapter 2 โ Current in a Magnetic Field
๐ช Force on a Current-Carrying Conductor: F = BIL
Put a wire carrying current inside a magnetic field and it gets pushed! This is the motor effect โ the principle behind every electric motor and loudspeaker.
๐ค Why Does the Wire Move?
The current in the wire creates its own magnetic field. This field interacts with the external magnetic field โ and the result is a FORCE on the wire. It's two magnetic fields fighting each other and pushing the wire out of the way.
๐ This is how a loudspeaker works! An alternating current flows through a coil in a magnetic field. The current changes direction 50 times a second โ force keeps reversing โ coil vibrates back and forth โ attached cone pushes air โ you hear sound!
๐ The Force on a Current-Carrying Conductor
A current-carrying conductor placed in a magnetic field experiences a force. The size of the force depends on: the magnetic flux density (B), the current (I), and the length of the conductor in the field (L).
โ ๏ธ Formula โ F = BIL (call it "BIL the Formula!")
F = BIL
F = force on the conductor (newtons, N)
B = magnetic flux density (tesla, T) โ how strong the field is
I = current flowing in the conductor (amps, A)
L = length of the conductor in the field (metres, m)
B = magnetic flux density (tesla, T) โ how strong the field is
I = current flowing in the conductor (amps, A)
L = length of the conductor in the field (metres, m)
๐ง Memory trick: Think of "BIL" as a person's name โ it's easy to remember! F = BIL. Write it on your hand before the exam ๐
๐ The Tesla โ Unit of Magnetic Flux Density
๐ Definition โ The Tesla
A magnetic flux density of one tesla will cause a current-carrying conductor of length 1 metre carrying a current of 1 amp to experience a force of 1 newton.
From F = BIL: B = F/(IL)
From F = BIL: B = F/(IL)
What Factors Affect the Force?
| Factor | Effect on force |
|---|---|
| Increase B (stronger magnet) | Force increases proportionally |
| Increase I (more current) | Force increases proportionally |
| Increase L (longer wire in field) | Force increases proportionally |
| Reverse current direction | Force reverses direction |
| Wire parallel to field (not perpendicular) | Force = zero |
Chapter 2 โ Current in a Magnetic Field
๐ค Fleming's Left Hand Rule
F = BIL tells us the SIZE of the force. Fleming's Left Hand Rule tells us the DIRECTION. You MUST know this for the exam!
๐๏ธ "Stick 'em up! I'm a left-handed FBI agent!"
Hold up your LEFT hand like you're being robbed (thumb and first two fingers all at 90ยฐ to each other):
๐ First finger (index) = B field direction
๐ Middle finger = I current direction
๐ Thumb = F orce direction (motion)
๐ง FBI Memory Trick: Force = thumb, B-field = First finger, I-current = Index+1 (middle finger). FBI โ Federal Bureau of Investigation! Or: Flying Bees Ignore... whatever works for you!
๐ฏ Devices that use this principle
Electric Motor
Current in rotating coil + magnetic field โ continuous force pushing coil around โ rotation โ mechanical energy
Loudspeaker
AC current through coil in field โ coil vibrates forwards and backwards โ cone moves โ sound waves produced
Galvanometer
Sensitive current meter that uses the force on a current-carrying coil to deflect a needle
Chapter 2 โ Current in a Magnetic Field
โ๏ธ Force on a Moving Charge: F = Bqv
What if the charge is not in a wire but is a free particle โ like an electron or proton? It still experiences a force!
A wire carrying current is really just charges (electrons) moving through it. So it makes sense that an individual moving charge in a magnetic field also experiences a force.
โ ๏ธ Formula โ Force on a Moving Charge (call it "BEV" โ like the name!)
F = Bqv
F = force (N)
B = magnetic flux density (T)
q = charge on the particle (C) โ for an electron: q = e = 1.6 ร 10โปยนโน C
v = velocity of the particle (m sโปยน)
B = magnetic flux density (T)
q = charge on the particle (C) โ for an electron: q = e = 1.6 ร 10โปยนโน C
v = velocity of the particle (m sโปยน)
๐ง "BIL and Bev" โ two names!
The two force formulas in this topic can be remembered as people's names: BIL (for conductor) and Bev (for moving charge). If you remember those two names, you remember both formulas!
The two force formulas in this topic can be remembered as people's names: BIL (for conductor) and Bev (for moving charge). If you remember those two names, you remember both formulas!
๐ Deriving F = Bqv from F = BIL
๐ Derivation
Show that F = Bqv can be derived from F = BIL
Start with F = BIL
Current I = q/t (charge per unit time)
Replace I
F = B ร (q/t) ร L
Velocity v = L/t, so L = vt
F = B ร (q/t) ร vt
The t cancels!
F = Bqv โ
โ
Derived: F = Bqv
๐ฏ Important Notes
- This formula applies to any charged particle โ electrons, protons, ions
- The particle must be moving โ a stationary charge experiences NO force
- The force is perpendicular to BOTH the velocity AND the field (use left hand rule)
- Because the force is always perpendicular to velocity, it doesn't speed the particle up โ it just changes its direction โ circular path!
Chapter 2 โ Current in a Magnetic Field
๐ต Circular Motion in a Magnetic Field
When a charged particle enters a magnetic field perpendicular to the field lines, it travels in a perfect circle. Here's how to calculate the radius!
Why a Circle?
The magnetic force (F = Bqv) is always perpendicular to the velocity. A force perpendicular to velocity doesn't change the speed โ it only changes the direction. An object with constant speed but constantly changing direction travels in a circle. The magnetic force IS the centripetal force!
๐ง Analogy: It's like swinging a ball on a string in a circle. The string (centripetal force) always pulls toward the centre โ perpendicular to the motion โ so the ball moves in a circle without speeding up or slowing down. The magnetic force plays the role of the string!
โ ๏ธ Equating Centripetal Force = Magnetic Force
Bqv = mvยฒ/r
Rearranging for radius: r = mv / (Bq)
For momentum p = mv: p = mv = Bqr
r = radius of circular path (m) m = mass (kg)
v = speed (m sโปยน) B = flux density (T) q = charge (C)
For momentum p = mv: p = mv = Bqr
r = radius of circular path (m) m = mass (kg)
v = speed (m sโปยน) B = flux density (T) q = charge (C)
Chapter 2 โ Current in a Magnetic Field
๐ The Magnetic Force Between Conductors & The Ampere
Two parallel wires carrying current each create magnetic fields โ and those fields interact, causing the wires to push or pull on each other!
โก Force Between Two Parallel Conductors
Two wires carrying current in the same direction attract each other. Two wires carrying current in opposite directions repel each other.
๐ง Memory trick: "Same direction = same friends = attract. Opposite direction = opposites push away = repel." Like lanes of traffic going the same way flow together, but traffic going opposite ways pushes apart!
๐ Definition โ The Ampere (SI unit of current)
The ampere is that constant current which, if flowing in two very long parallel wires one metre apart in a vacuum, will experience a force of 2 ร 10โปโท N per metre length.
๐งช Demonstrating the Principle
๐ฏ Experiment:
Connect two thin parallel aluminium strips in a circuit as shown. Switch on the current. The strips move towards each other (if currents are in the same direction) or repel (if opposite directions). This directly demonstrates the principle behind the definition of the ampere.
Connect two thin parallel aluminium strips in a circuit as shown. Switch on the current. The strips move towards each other (if currents are in the same direction) or repel (if opposite directions). This directly demonstrates the principle behind the definition of the ampere.
Chapter 2 โ Worked Examples
๐ Calculations: Chapter 2
F = BIL and F = Bqv worked step by step โ with every exam trick explained.
๐งฎ Example 1 โ Basic F = BIL (OL)
Q: A conductor of length 50 cm carries a current of 5 A in a magnetic field of flux density 3 T. Calculate the force.
Write down values (ALWAYS convert units!)
L = 50 cm = 0.5 m, I = 5 A, B = 3 T
Apply F = BIL
F = BIL = (3)(5)(0.5) = 7.5 N
โ
Force = 7.5 N
๐งฎ Example 2 โ Finding B from F = BIL (HL)
Q: A wire (length 20 cm) in a field carries 55 mA. Maximum force = 130 ฮผN. Find the magnetic flux density B.
Convert ALL units to SI first!
F = 130 ฮผN = 130 ร 10โปโถ N
I = 55 mA = 0.055 A
L = 20 cm = 0.2 m
I = 55 mA = 0.055 A
L = 20 cm = 0.2 m
Rearrange F = BIL for B
B = F / (IL) = (130 ร 10โปโถ) / (0.055 ร 0.2)
Calculate
B = (130 ร 10โปโถ) / 0.011 = 0.0118 T
โ
B = 0.0118 T โ 11.8 mT
๐งฎ Example 3 โ Circular Path Radius (HL)
Q: An electron (speed = 1.45 ร 10โธ m sโปยน) travels in a magnetic field of B = 90 mT. Find the radius of its circular path. (m_e = 9.1 ร 10โปยณยน kg, e = 1.6 ร 10โปยนโน C)
Equate magnetic force = centripetal force
Bqv = mvยฒ/r
Rearrange: r = mv / (Bq)
Rearrange: r = mv / (Bq)
Substitute values
r = (9.1 ร 10โปยณยน ร 1.45 ร 10โธ) / (90 ร 10โปยณ ร 1.6 ร 10โปยนโน)
Calculate numerator and denominator
Numerator: 9.1 ร 10โปยณยน ร 1.45 ร 10โธ = 1.3195 ร 10โปยฒยฒ
Denominator: 90 ร 10โปยณ ร 1.6 ร 10โปยนโน = 1.44 ร 10โปยฒโฐ
r = 1.3195 ร 10โปยฒยฒ / 1.44 ร 10โปยฒโฐ = 9.16 ร 10โปยณ m
Denominator: 90 ร 10โปยณ ร 1.6 ร 10โปยนโน = 1.44 ร 10โปยฒโฐ
r = 1.3195 ร 10โปยฒยฒ / 1.44 ร 10โปยฒโฐ = 9.16 ร 10โปยณ m
โ
Radius = 9.16 ร 10โปยณ m = 9.16 mm
๐งฎ Example 4 โ Finding Speed from Circular Path (HL)
Q: A proton enters a field B = 0.5 T in a circular path of radius 2.3 mm. Find its speed. (m_p = 1.67 ร 10โปยฒโท kg, q = 1.6 ร 10โปยนโน C)
From Bqv = mvยฒ/r, rearrange for v
Bq = mv/r โ v = Bqr/m
Substitute
v = (0.5 ร 1.6 ร 10โปยนโน ร 2.3 ร 10โปยณ) / (1.67 ร 10โปยฒโท)
v = (1.84 ร 10โปยฒยฒ) / (1.67 ร 10โปยฒโท)
v = 1.1 ร 10โต m sโปยน
v = (1.84 ร 10โปยฒยฒ) / (1.67 ร 10โปยฒโท)
v = 1.1 ร 10โต m sโปยน
โ
Speed = 1.1 ร 10โต m sโปยน (110 km/s!)
Chapter 2 โ Quiz
โ Quiz: Chapter 2
Test yourself on magnetic forces, F=BIL, and Fleming's Left Hand Rule!
Chapter 3 โ Electromagnetic Induction
๐ Magnetic Flux: ฮฆ = BA
Before we can understand Faraday's Law and induced voltage, we need to understand magnetic flux. Think of it as "how much magnetic field is passing through a loop".
๐ Definition โ Magnetic Flux (ฮฆ)
Magnetic flux is defined as the product of magnetic flux density (B) and the cross-sectional area (A) perpendicular to the direction of the magnetic flux density. ฮฆ = BA. Unit: weber (Wb).
โ ๏ธ Magnetic Flux Formula
ฮฆ = BA
ฮฆ (phi, pronounced "fy") = magnetic flux (webers, Wb)
B = magnetic flux density (tesla, T)
A = area perpendicular to the field (mยฒ)
B = magnetic flux density (tesla, T)
A = area perpendicular to the field (mยฒ)
๐ A Great Analogy โ Water Flow!
๐ Imagine rain falling into a bucket.
โข The magnetic flux is like the total amount of rain going INTO the bucket per second
โข B (flux density) is like how heavy the rain is (how many drops per mยฒ)
โข A is the opening area of the bucket
โข If you tilt the bucket sideways so rain hits the side โ less rain goes in! That's why A must be the area PERPENDICULAR to the field.
โข ฮฆ is MAXIMUM when the field is straight through the loop (perpendicular to the area)
โข ฮฆ = ZERO when the field runs parallel to the plane of the loop (goes in one side and out the other โ nothing "through" it)
โข The magnetic flux is like the total amount of rain going INTO the bucket per second
โข B (flux density) is like how heavy the rain is (how many drops per mยฒ)
โข A is the opening area of the bucket
โข If you tilt the bucket sideways so rain hits the side โ less rain goes in! That's why A must be the area PERPENDICULAR to the field.
โข ฮฆ is MAXIMUM when the field is straight through the loop (perpendicular to the area)
โข ฮฆ = ZERO when the field runs parallel to the plane of the loop (goes in one side and out the other โ nothing "through" it)
Left: field passes straight through the loop โ maximum flux. Right: field parallel to loop โ zero flux passes through.
Chapter 3 โ Electromagnetic Induction
โก Faraday's Law & Induced EMF
Move a magnet near a coil and you get electricity! Faraday's Law tells us exactly how much voltage is produced.
๐ Definition โ Electromagnetic Induction
Electromagnetic induction occurs when an emf is induced in a coil due to a changing magnetic flux.
๐ Faraday's Law
The size of the induced emf is proportional to the rate of change of magnetic flux.
โ ๏ธ Formula โ Induced EMF
emf = N ร (ฮฮฆ / ฮt)
emf = induced voltage (volts, V)
N = number of turns in the coil
ฮฮฆ = change in magnetic flux = (final flux โ initial flux) (Wb)
ฮt = time taken for the change (s)
Remember: for one turn (N=1): emf = ฮฮฆ/ฮt
N = number of turns in the coil
ฮฮฆ = change in magnetic flux = (final flux โ initial flux) (Wb)
ฮt = time taken for the change (s)
Remember: for one turn (N=1): emf = ฮฮฆ/ฮt
๐ง Key insight โ what causes a BIGGER emf?
1. Move faster โ less time โ bigger rate of change of flux โ bigger emf
2. More turns (N) โ each turn gets an emf, they add up
3. Stronger magnet โ bigger B โ bigger flux change โ bigger emf
The emf is ZERO when the magnet is completely still โ no CHANGE in flux = no emf!
1. Move faster โ less time โ bigger rate of change of flux โ bigger emf
2. More turns (N) โ each turn gets an emf, they add up
3. Stronger magnet โ bigger B โ bigger flux change โ bigger emf
The emf is ZERO when the magnet is completely still โ no CHANGE in flux = no emf!
๐งช Demonstrating Electromagnetic Induction
๐ฏ Experiment:
Connect a coil of wire to a galvanometer (sensitive current meter). Move a bar magnet into the coil โ the needle deflects. Stop the magnet โ needle returns to zero. Move it out โ needle deflects the other way. Move it faster โ bigger deflection. This shows: changing flux โ induced emf โ current โ deflection.
Connect a coil of wire to a galvanometer (sensitive current meter). Move a bar magnet into the coil โ the needle deflects. Stop the magnet โ needle returns to zero. Move it out โ needle deflects the other way. Move it faster โ bigger deflection. This shows: changing flux โ induced emf โ current โ deflection.
Chapter 3 โ Electromagnetic Induction
๐ Lenz's Law
Faraday's Law tells us the SIZE of the induced emf. Lenz's Law tells us the DIRECTION. And it has a beautiful, simple principle behind it.
๐ Lenz's Law
The direction of the induced emf is always such as to oppose the change producing it.
๐ง Simple version: Nature is lazy and resistant to change! If you push a magnet INTO a coil, the coil fights back by becoming a magnet that pushes the original magnet away. If you PULL the magnet out, the coil tries to hold it in. The induced current always opposes whatever you're doing!
โก This is a consequence of conservation of energy! If the induced current helped the change (instead of opposing it), you'd get more energy out than you put in โ that would be a perpetual motion machine, which is impossible!
๐ฅ Lenz's Law Demonstration 1: Copper Tube
๐ฏ Apparatus: Copper pipe, plastic pipe, strong neodymium magnet
Procedure: Drop the magnet down BOTH tubes. Time how long each takes.
Observation: Magnet falls much SLOWER through the copper tube than through the plastic tube.
Explanation:
1. Falling magnet creates CHANGING magnetic flux in both tubes
2. Changing flux โ induced emf in both tubes
3. Current only flows in COPPER (it's a conductor โ plastic is an insulator, so no current in plastic)
4. Induced current in copper creates a magnetic field that OPPOSES the fall (Lenz's Law) โ magnet slows down
5. Plastic: no current โ no opposing field โ normal gravity speed
Procedure: Drop the magnet down BOTH tubes. Time how long each takes.
Observation: Magnet falls much SLOWER through the copper tube than through the plastic tube.
Explanation:
1. Falling magnet creates CHANGING magnetic flux in both tubes
2. Changing flux โ induced emf in both tubes
3. Current only flows in COPPER (it's a conductor โ plastic is an insulator, so no current in plastic)
4. Induced current in copper creates a magnetic field that OPPOSES the fall (Lenz's Law) โ magnet slows down
5. Plastic: no current โ no opposing field โ normal gravity speed
๐ฅ Lenz's Law Demonstration 2: Aluminium Ring
๐ฏ Apparatus: Aluminium ring suspended by thread, bar magnet
Move magnet TOWARDS ring: Ring moves AWAY (opposes approach)
Move magnet AWAY from ring: Ring follows/chases the magnet (opposes departure)
Explanation: Moving magnet โ changing flux โ induced current in ring โ ring's magnetic field opposes the change. The ring and magnet act like same-pole magnets (repel) when approaching, and opposite-pole magnets (attract) when separating.
Move magnet TOWARDS ring: Ring moves AWAY (opposes approach)
Move magnet AWAY from ring: Ring follows/chases the magnet (opposes departure)
Explanation: Moving magnet โ changing flux โ induced current in ring โ ring's magnetic field opposes the change. The ring and magnet act like same-pole magnets (repel) when approaching, and opposite-pole magnets (attract) when separating.
Chapter 3 โ Electromagnetic Induction
๐ Electric Generators & Alternating Current
Generators use electromagnetic induction to convert movement into electricity. They power your home right now!
๐ Definition โ Electric Generator
An electric generator is a device that converts mechanical (kinetic) energy to electrical energy, using electromagnetic induction.
โ๏ธ How a Generator Works
A coil of wire rotates inside a magnetic field. As the coil rotates, the magnetic flux through it keeps changing โ which induces an emf by Faraday's Law. The coil is connected to an external circuit through slip rings and brushes.
- When coil is perpendicular to field โ flux changing fastest โ maximum emf
- When coil is parallel to field โ flux = 0, not changing โ emf = 0
- As coil rotates, emf oscillates โ alternating current (AC)
๐ Definition โ Alternating Current (AC)
Alternating current is current which continually changes direction. Mains electricity in Ireland changes direction 50 times per second (50 Hz).
๐ RMS Values โ Making AC Comparable to DC
AC voltage constantly changes from positive to negative. To compare it fairly with DC, we use the Root Mean Square (RMS) value โ the DC equivalent that produces the same power.
โ ๏ธ RMS Formulas
V_rms = V_max / โ2 I_rms = I_max / โ2
V_rms = RMS voltage (effective voltage, V)
V_max = peak (maximum) voltage (V)
โ2 โ 1.414
Ireland mains: V_max โ 325 V โ V_rms = 325/โ2 โ 230 V โ
V_max = peak (maximum) voltage (V)
โ2 โ 1.414
Ireland mains: V_max โ 325 V โ V_rms = 325/โ2 โ 230 V โ
๐ง Why do we use RMS? An AC current of I_rms produces the same HEATING EFFECT as a DC current of the same value. So a 230V AC supply heats your kettle the same as a 230V DC supply would. RMS makes AC and DC directly comparable for power calculations.
๐ The Microphone
A microphone works on the same principle as a generator but in reverse (kind of). Sound waves vibrate a coil inside a magnetic field. The coil moves โ changing flux โ induced emf โ electrical signal that represents the sound.
Chapter 3 โ Electromagnetic Induction
๐ก Mutual Induction & Transformers
Two coils near each other can transfer energy without any direct electrical connection โ that's mutual induction. A transformer uses this to change voltage!
๐ Mutual Induction
Mutual induction occurs when an alternating current in one coil results in an induced emf in a second nearby coil, due to the changing magnetic flux linking both coils.
๐ How a Transformer Works
A transformer has two coils wound around the same soft iron core:
- Primary coil โ connected to AC input voltage
- Secondary coil โ produces the output voltage
- Soft iron core โ channels the magnetic flux from primary to secondary efficiently
AC in primary โ changing current โ changing B field โ changing flux in iron core โ changing flux in secondary โ induced emf in secondary. The output voltage depends on the ratio of turns!
โ ๏ธ Transformer Equation
Vs / Vp = Ns / Np
Vs = voltage across secondary coil (output)
Vp = voltage across primary coil (input)
Ns = number of turns on secondary coil
Np = number of turns on primary coil
Vp = voltage across primary coil (input)
Ns = number of turns on secondary coil
Np = number of turns on primary coil
Step-UP Transformer
Ns > Np
More turns on secondary โ higher output voltage. Used in power stations to step voltage UP to 400,000V for transmission.
Step-DOWN Transformer
Ns < Np
Fewer turns on secondary โ lower output voltage. Used to step voltage DOWN to 230V for homes.
๐ก Why transmit at HIGH voltage? P = IยฒR โ heat loss in cables depends on CURRENT SQUARED. Transmit at high voltage โ low current โ much less heat wasted. Transformers make this possible โ hence they're essential to modern electricity grids!
๐ง Making Transformers More Efficient
- Laminated iron core โ thin sheets of iron insulated from each other. Reduces eddy currents (circular currents that would otherwise waste energy as heat in the core)
- Soft iron core โ easy to magnetise and de-magnetise rapidly with the AC. Hard steel would resist the changing field and waste energy
๐งช Demonstrating a Transformer
๐ฏ Experiment:
Set up two coils on the same soft iron core. Connect the primary to an AC supply and measure the secondary voltage with a voltmeter. Observation: a continuous voltage reading is obtained. The size of the induced emf increases when the coils are wound closer together and when they share the same iron core.
Set up two coils on the same soft iron core. Connect the primary to an AC supply and measure the secondary voltage with a voltmeter. Observation: a continuous voltage reading is obtained. The size of the induced emf increases when the coils are wound closer together and when they share the same iron core.
Chapter 3 โ Electromagnetic Induction
๐ Self-Induction & Inductors
A coil can induce a voltage in ITSELF when the current changes. This "back-emf" fights against the changing current โ and it's why coils are used to limit AC in circuits!
๐ค What is Self-Induction?
When AC flows through a coil, the current is constantly changing. This changing current creates a changing magnetic field in the coil itself. By Faraday's Law, this changing field induces an emf in the very same coil โ but by Lenz's Law, this emf OPPOSES the original change in current. It's called back-emf.
๐ง Analogy: Imagine trying to push a heavy door. The door has inertia โ it resists your push at first. Self-induction gives a coil "electrical inertia" โ it resists changes in current. A coil doesn't want the current to change suddenly!
๐ฌ Demonstrating Self-Induction (Back EMF)
๐ฏ Experiment:
Apparatus: 6V AC supply, coil (1200 turns), soft iron core, 6V filament lamp
Procedure:
1. Connect lamp + coil in series with the AC supply. Switch on โ lamp lights.
2. Slowly insert the soft iron core into the coil โ lamp gets DIMMER.
Explanation:
โข AC produces a changing magnetic field in the coil โ induces a back-emf
โข This back-emf opposes the applied voltage โ reduces the effective current โ lamp dims
โข Iron core increases flux โ larger back-emf โ less current โ lamp even dimmer
Important: This ONLY works with AC! With DC, the current isn't changing, so there's no changing flux, no back-emf, and the lamp stays bright even with the iron core inserted.
Apparatus: 6V AC supply, coil (1200 turns), soft iron core, 6V filament lamp
Procedure:
1. Connect lamp + coil in series with the AC supply. Switch on โ lamp lights.
2. Slowly insert the soft iron core into the coil โ lamp gets DIMMER.
Explanation:
โข AC produces a changing magnetic field in the coil โ induces a back-emf
โข This back-emf opposes the applied voltage โ reduces the effective current โ lamp dims
โข Iron core increases flux โ larger back-emf โ less current โ lamp even dimmer
Important: This ONLY works with AC! With DC, the current isn't changing, so there's no changing flux, no back-emf, and the lamp stays bright even with the iron core inserted.
๐ Definition โ Inductor
An inductor is an electrical component (a coil) used to reduce the flow of alternating current. It works by self-induction โ the back-emf it creates opposes the AC current.
Example: The dimmer switch in stage lighting uses an inductor to reduce the current through the bulb, making it dimmer. Much more efficient than a resistor (which wastes energy as heat).
Chapter 3 โ Worked Examples
๐ Calculations: Chapter 3
Magnetic flux, induced emf, transformers, and RMS values โ all worked step by step.
๐งฎ Example 1 โ Magnetic Flux (ฮฆ = BA)
Q: A square coil of side 5 cm lies perpendicular to a magnetic field of 4.0 T. What is the magnetic flux cutting the coil?
Find the area of the coil
A = (0.05)ยฒ = 0.0025 mยฒ (always convert cm โ m first!)
Use ฮฆ = BA
ฮฆ = 4.0 ร 0.0025 = 0.01 Wb
โ
Magnetic flux = 0.01 Wb
๐งฎ Example 2 โ Induced EMF (straightforward)
Q: A coil of 150 turns has flux increasing by 4.5 ร 10โปโด Wb in 3 ms. Find the average induced emf.
Write values
N = 150 turns, ฮฮฆ = 4.5 ร 10โปโด Wb, ฮt = 3 ร 10โปยณ s
emf = N ร (ฮฮฆ / ฮt)
emf = 150 ร (4.5 ร 10โปโด) / (3 ร 10โปยณ)
emf = 150 ร 0.15 = 22.5 V
emf = 150 ร 0.15 = 22.5 V
โ
Induced emf = 22.5 V
๐งฎ Example 3 โ Induced EMF (coil rotated 90ยฐ)
Q: A 40-turn square coil (side 20 cm) is perpendicular to B = 50 mT. It is rotated 90ยฐ in 0.25 s. Find the average induced emf.
Find initial flux (coil perpendicular to field = max flux)
A = (0.2)ยฒ = 0.04 mยฒ
ฮฆ_initial = BA = (50 ร 10โปยณ)(0.04) = 2 ร 10โปยณ Wb
ฮฆ_initial = BA = (50 ร 10โปยณ)(0.04) = 2 ร 10โปยณ Wb
Final flux (coil parallel to field = zero flux)
ฮฆ_final = 0 Wb (field is now parallel to plane of coil)
emf = N ร (ฮฮฆ / ฮt)
emf = 40 ร (2 ร 10โปยณ - 0) / 0.25
emf = 40 ร 0.008 = 0.32 V
emf = 40 ร 0.008 = 0.32 V
โ
Induced emf = 0.32 V
๐งฎ Example 4 โ Transformer Calculation (OL)
Q: A transformer has 150 turns on the primary and 3000 turns on the secondary. Input = 12 V AC. Find the output voltage.
Write Vs/Vp = Ns/Np
Vs / 12 = 3000 / 150
Solve for Vs
Vs = (3000/150) ร 12 = 20 ร 12 = 240 V
โ
Output voltage = 240 V (step-UP transformer โ secondary has more turns)
๐งฎ Example 5 โ RMS Voltage
Q: An AC supply has peak voltage of 300 V. Calculate the RMS voltage.
V_rms = V_max / โ2
V_rms = 300 / โ2 = 300 / 1.414 = 212.1 V
โ
V_rms โ 212 V (The 230V Irish mains โ V_max โ 325V)
๐งฎ Example 6 โ Moving Loop (HL โ tricky!)
Q: A square loop (side 5 cm) enters a field B = 8 T at speed 5 m sโปยน. (a) Time to enter fully? (b) Flux when fully inside? (c) Average induced emf while entering?
(a) time = distance/speed
Distance to enter = side length = 0.05 m
time = 0.05 / 5 = 0.01 s
time = 0.05 / 5 = 0.01 s
(b) ฮฆ = BA when fully inside
A = (0.05)ยฒ = 0.0025 mยฒ
ฮฆ = 8 ร 0.0025 = 0.02 Wb
ฮฆ = 8 ร 0.0025 = 0.02 Wb
(c) emf = ฮฮฆ / ฮt (N = 1 turn)
ฮฮฆ = 0.02 - 0 = 0.02 Wb (flux goes from 0 to 0.02 Wb)
emf = 0.02 / 0.01 = 2 V
emf = 0.02 / 0.01 = 2 V
โ
(a) 0.01 s (b) 0.02 Wb (c) 2 V
Chapter 3 โ Quiz
โ Quiz: Chapter 3
Test yourself on electromagnetic induction, Faraday's Law, Lenz's Law, and transformers!
๐ All Formulas โ Quick Reference
Every formula you need for the Electricity & Magnetism Leaving Cert exam. Highlighted ones are Higher Level only.
Chapter 2 โ Current in a Magnetic Field
Force on a conductor
F = BIL
F=force (N), B=flux density (T), I=current (A), L=length in field (m)
Force on a moving charge
F = Bqv
B=flux density (T), q=charge (C), v=velocity (m sโปยน)
โญ Circular path (HL) โ equate centripetal = magnetic
Bqv = mvยฒ/r โ r = mv/(Bq)
Also: momentum p = mv = Bqr
Chapter 3 โ Electromagnetic Induction
Magnetic flux
ฮฆ = BA
ฮฆ=flux (Wb, webers), B=flux density (T), A=area perpendicular to field (mยฒ)
โญ Faraday's Law โ induced emf
emf = N ร (ฮฮฆ / ฮt)
N=number of turns, ฮฮฆ=change in flux (Wb), ฮt=time (s)
Transformer equation
Vs / Vp = Ns / Np
Vs=secondary voltage, Vp=primary voltage, Ns=secondary turns, Np=primary turns
RMS values (AC)
V_rms = V_max / โ2 I_rms = I_max / โ2
Electron charge (e)
1.6ร10โปยนโน C
Electron mass (mโ)
9.1ร10โปยณยน kg
Proton mass (mโ)
1.67ร10โปยฒโท kg
โ2
โ 1.414
Used in V_rms = V_max/โ2
โญ Higher Level formulas are marked with a star. The main HL additions are: circular path in a magnetic field (Bqv = mvยฒ/r) and the induced emf formula (emf = Nยทฮฮฆ/ฮt). Everything else is needed by all students!
๐ All Definitions โ Learn These Off!
These are the definitions you need to be able to write word-for-word in the exam. The key words are bolded.
Chapter 1 โ Magnets & Fields
Magnetic Field
A magnetic field is any region of space where magnetic forces can be felt.
Chapter 2 โ Current in a Magnetic Field
The Tesla (unit of magnetic flux density)
A magnetic flux density of one tesla will cause a current-carrying conductor of length 1 metre carrying a current of 1 amp to experience a force of 1 newton. B = F/(IL)
The Ampere (SI unit of current)
The ampere is that constant current which, if flowing in two very long parallel wires one metre apart in a vacuum, will experience a force of 2 ร 10โปโท N per metre length.
Chapter 3 โ Electromagnetic Induction
Electromagnetic Induction
Electromagnetic induction occurs when an emf is induced in a coil due to a changing magnetic flux.
Magnetic Flux (ฮฆ)
Magnetic flux is defined as the product of magnetic flux density and the cross-sectional area perpendicular to the direction of the magnetic flux density. ฮฆ = BA. Unit: weber (Wb).
Faraday's Law
Faraday's Law states that the size of the induced emf is proportional to the rate of change of magnetic flux.
Lenz's Law
Lenz's Law states that the direction of the induced emf is always such as to oppose the change producing it.
Electric Generator
An electric generator is a device that converts mechanical (kinetic) energy to electrical energy.
Alternating Current (AC)
Alternating current is current which continually changes direction. Irish mains = 50 Hz (changes direction 50 times per second).
Inductor
An inductor is an electrical component (coil) used to reduce the flow of alternating current, using the principle of self-induction.
emf (electromotive force)
emf (electromotive force) is a potential difference applied to a complete circuit. It is the voltage that drives current around a circuit.
๐ฏ Exam tip: The bolded words above are the ones examiners look for. Missing a key word (like "perpendicular" in the flux definition, or "oppose" in Lenz's Law, or "rate of change" in Faraday's Law) will cost you marks. Learn the exact wording!