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20.4.1Magnetic fields and alternating currents (A Level)

Magnetic Fields in Wires, Coils and Solenoids

5 min read 10 parts Lesson 12 of 24 1 quiz

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Lesson summary

20.4.1 Magnetic Fields in Wires, Coils and Solenoids — AS PHYSICS 9702 notes: Describe and calculate the magnetic fields of a long wire, a flat circular coil and a long solenoid.Source — moving charge creates a magnetic field, formed wherever a current flowsLong straight wire — f…

  • Reversing the current
  • Dependence
  • Equivalence
  • Centre field
  • Inside the solenoid
  • More turns

Section 1 of 10Currents make magnetic fields

Source
  • Source moving charge creates a magnetic field, formed wherever a current flows
Long straight wire
  • Long straight wire field lines are concentric circles centred on the wire, in planes perpendicular to it
Direction
  • Direction the right-hand grip rule, with the thumb along the conventional current and the curled fingers along the field
Strength
  • Strength lines are closer near the wire, where the field is stronger, and further apart far away
Reversing the current
  • Reversing the current reverses the field
Size
  • Size the field of a wire is weak, with 10 A giving only 2 × 10⁻⁵ T at 10 cm

Section 2 of 10Long straight wire

Equation
  • B = μ₀I/(2πr)
  • r is the perpendicular distance in m
  • μ₀ = 4π × 10⁻⁷ H m⁻¹ is the permeability of free space
Dependence
  • B is inversely proportional to distance, so doubling I doubles B and doubling r halves it
Graphs
  • B against r is a reciprocal curve, and B against 1/r is a straight line through the origin with gradient μ₀I/2π

Section 3 of 10Flat circular coil

Equivalence
  • Equivalence a flat coil is like one turn of a solenoid, and the field lines pass through the loop
Poles
  • Poles the face the field leaves is a north pole and the other face is a south pole
  • Seen face-on, an anticlockwise current gives a north pole and a clockwise current a south pole
Centre field
  • B = μ₀NI/(2r) for N turns of radius r, perpendicular to the plane
Dependence
  • Dependence it grows with N and I and falls as the coil gets bigger

Section 4 of 10Long solenoid

Inside the solenoid
  • Inside the solenoid an almost uniform field parallel to the axis, with parallel equally spaced lines
Outside
  • Outside a weak field like that of a bar magnet
Equation
  • B = μ₀nI with n = N/L, the number of turns per metre
Independence
  • Independence the field depends on turn density, not diameter
Ends
  • Ends the field at the ends is about half the central value because the lines fan out
Poles
  • Poles curled fingers follow the current and the thumb points to the north end

Section 5 of 10Strengthening the field

1Iron core
  • Iron core a ferrous core becomes magnetised and can increase B several hundred times
2More turns
  • More turns they concentrate the field lines
3Stretching a coil
  • Stretching a coil the same turns over more length lowers n and so B
4Compressing
  • Compressing raises B
5Scaling
  • Scaling doubling the current doubles B, and doubling both turns and length leaves B unchanged because n is the same

Section 6 of 10Field problems

1Several sources
  • Several sources treat B as a vector and add contributions using directions from the grip rule
2Between two wires with opposite currents
  • Between two wires with opposite currents the contributions add, whereas on the outside at the same distance they subtract
3Wire through a coil
  • Wire through a coil add components at right angles with Pythagoras
4Units
  • μ₀nI gives tesla when n is in m⁻¹ and I in A

Section 7 of 10Applications

Electromagnets
  • Electromagnets relays, loudspeakers, scrap-metal cranes and MRI scanners use solenoids
Hall probe
  • Hall probe the standard instrument for checking a coil's field, with probe reading against current a straight line through the origin
Force between wires
  • Force between wires the same field equations underlie the force between parallel conductors
Drawing
  • Drawing put an arrow on every field line and keep lines in a uniform field equally spaced

Section 8 of 10More from the specification

1Magnetic Field Lines Around Current-Carrying Conductors
  • An electric current flowing through a straight wire produces concentric circular magnetic field lines around the conductor;
    • their direction is determined by the right-hand grip rule, shown with directional arrows.
2Magnetic Interaction Between Parallel Conductors
  • Two parallel current-carrying conductors exert mutual magnetic forces on one another: when currents flow in the same direction, their magnetic fields combine to make the wires attract;
  • when currents flow in opposite directions, the wires repel.
3Magnetic Field of Coils and Solenoids
  • Adding multiple loops into a cylindrical solenoid produces a strong, uniform axial magnetic field inside that closely resembles the dipolar magnetic field of a permanent bar magnet.
4Concentric magnetic field lines
  • Concentric magnetic field lines field lines around a straight current-carrying conductor form concentric circles with spacing increasing outwards.
5Right-hand grip rule
  • Right-hand grip rule right-hand thumb points along current while curled fingers determine direction arrows of magnetic flux lines.
6Parallel conductor forces
  • Parallel conductor forces two parallel current-carrying conductors attract if currents flow in the same direction and repel if opposite.
7Attract
  • Pull together.
8Magnetic force
  • The force on a moving charge in a magnetic field

Section 9 of 10Key terms

TermMeaning
Right-hand grip rulethumb along conventional current, curled fingers give the field direction
Permeability of free spaceμ₀ = 4π × 10⁻⁷ H m⁻¹
Solenoida long coil of wire carrying current
Turn densityn = N/L, turns per metre
Ferromagnetic coreiron that concentrates flux and strengthens the field
Electromagneta magnet produced by current in a coil

Section 10 of 10Exam technique

1
Using the left hand for the grip rule — use the right hand.
2
Using the direction of electron flow — use conventional current.
3
Forgetting that n is turns per metre — n = N/L.
4
Missing the arrows on field lines — draw arrows on every line.
Transformer Golden Equations Physics Standard

Transformer Turns Ratio & Efficiency

Ratio: Vp / Vs = Np / Ns = Is / Ip

  • Step-up reduces grid thermal loss (P = I2R).
  • Laminated core prevents eddy currents.