Skip to content
Dabour HubLEARN · PRACTICE · EXPLORESign inStudent

Theme D — Fields

D.3 Motion in Electromagnetic Fields — IB Physics HL Revision Notes & Topical Questions

5 min read 11 parts Lesson 27 of 39 1 quiz

📚 IB Physics HL Hub / Topical Revision
🩺
100% Curriculum Specification Match Lesson Doctor Verified
The only platform with 100% curriculum specification match and verified interactive question banks.
0%read
Lesson summary

D.3 Motion in Electromagnetic Fields — IB PHYSICS HL notes: Calculate magnetic forces on conductors, parallel wires and moving charges and analyse charged-particle motion in electric and magnetic fields.Equation — F = BIL sin θ, with θ the angle between the conductor and the fiel…

  • What the symbols mean
  • Increase the force
  • Demonstration
  • Mutually perpendicular
  • Fleming's left-hand rule
  • Conventional current

Part 1 of 9Force on a current-carrying conductor

Equation
  • F = BIL sin θ, with θ the angle between the conductor and the field
    What the symbols mean: F = force on the wire (N) · B = magnetic flux density (T) · I = current (A) · L = length of wire in the field (m) · θ = angle between wire and field
Symbols
  • F in N, B in T, I in A and L, the length of conductor inside the field, in m
Increase the force
  • Increase the force raise B, I or the length in the field
Maximum
  • F = BIL when the conductor is perpendicular to the field (θ = 90°)
Zero
  • F = 0 when the current is parallel to the field (θ = 0°)
Tesla
  • 1 T = 1 N A−1 m−1
Demonstration
  • Demonstration a copper rod in a field accelerates when current passes through it

Part 2 of 9Direction of the force

Mutually perpendicular
  • F, B and I are at right angles
Fleming's left-hand rule
  • Fleming's left-hand rule thumb gives force or motion, first finger the field and second finger the conventional current
Conventional current
  • Conventional current positive to negative, opposite to electron flow
Diagram symbols
  • Diagram symbols dots show a field out of the page and crosses show a field into the page
Motor rule
  • Motor rule the left-hand rule is for motors and the right-hand rule is for generators

Part 3 of 9Force between parallel conductors

Cause
  • Cause each wire lies in the magnetic field of the other
Same direction
  • Same direction the currents attract
Opposite directions
  • Opposite directions the currents repel
Equal and opposite
  • Equal and opposite the forces on the two wires are equal in size and opposite in direction
Force per unit length
  • F/L = μ0I1I2/2πr
  • μ0 = 4π × 10−7 N A−2 and r is the wire separation
Derivation
  • Derivation the field of wire 2 at wire 1 is B2 = μ0I2/2πr and F/L = B2I1

Part 4 of 9Force on a moving charge

Equation
  • F = Bqv sin θ
Maximum
  • F = Bqv when the particle moves perpendicular to the field
Zero
  • Zero no force for a stationary particle or one moving parallel to the field
Perpendicular
  • F is perpendicular to both v and B
Direction
  • Direction use the left-hand rule with the second finger along the velocity for a positive charge and opposite to the velocity for a negative charge
Do not mix up
  • F = BIL is for a conductor and F = Bqv for an isolated moving charge

Part 5 of 9Circular motion in a magnetic field

Circular motion in a magnetic field
Path
  • Path the force is always perpendicular to the velocity so the particle follows a circle at constant speed
No work
  • No work the magnetic force does no work
Centripetal force
  • Bqv = mv2/r
Radius
  • Radius r = mv/Bq
Dependence
  • Dependence larger speed or mass gives a larger circle
  • Greater charge or field gives a smaller circle
Period
  • T = 2πm/Bq, independent of speed
Parallel component
  • Parallel component a component of velocity along the field is unchanged

Part 6 of 9Charged particles in an electric field

Charged particles in an electric field
Force
  • F = qE, constant in size and direction in a uniform field
Acceleration
  • Acceleration a = qE/m
Starting at rest
  • Starting at rest the particle moves along the field lines, with positive charge along the field and negative charge against it
Entering perpendicular to the field
  • Entering perpendicular to the field the original velocity component is unchanged and the particle accelerates along the field, giving a parabolic path
Direction
  • Direction a positive charge is deflected towards the negative plate and a negative one towards the positive plate
Neutron
  • Neutron it is undeflected
Deflection
  • Deflection greater for larger charge, smaller for larger mass and smaller for larger speed

Part 7 of 9Crossed electric and magnetic fields

Forces
  • Forces for perpendicular E and B the electric and magnetic forces act in opposite directions on a particle
Condition
  • Condition qE = Bqv gives a straight path at constant speed
Velocity selector
  • Velocity selector v = E/B for particles of a single speed
  • E = V/d between the plates
Sign of charge
  • Sign of charge both forces reverse for a negative charge, so the balance condition is the same

Part 8 of 9Charge-to-mass ratio

1
Definition
  • Definition q/m, the ratio of the charge to the mass of the particle
2
Electron
  • Electron e/me = 1.76 × 1011 C kg−1
3
Proton
  • Proton e/mp = 9.58 × 107 C kg−1
4
Thomson's apparatus
  • Helmholtz coils give a uniform magnetic field and parallel plates a uniform electric field
5
Step 1
  • Step 1 adjust V until the beam is straight, giving v = V/Bd
6
Step 2
  • Step 2 switch off the electric field so the beam moves in a circle of radius r
7
Step 3
  • Step 3 combine r = mv/Bq and v = V/Bd to get q/m = V/(rB2d)

Part 9 of 9More from the specification

1Magnetic Force on a Current-Carrying Conductor
  • A straight current-carrying conductor oriented perpendicular to a magnetic field experiences a mechanical force given by F = B * I * L,
  • where B represents the magnetic field strength (flux density).
2Thomson's Charge-to-Mass Ratio Experiment
  • By balancing electrostatic force (qE) and magnetic force (qvB) in crossed fields, J.J.
  • Thomson measured particle velocity and determined the charge-to-mass ratio (q / m) of the electron.
3Charged Nuclei in Magnetic Fields
  • When an ionized particle such as a boron nucleus enters a magnetic field, the centripetal magnetic force curves its trajectory into a circle whose radius (r = m * v / (B * q)) depends on its specific charge-to-mass ratio.
4Magnetic Flux Density Definition
  • Magnetic field strength B is defined as the force per unit current per unit length acting on a current-carrying conductor placed perpendicular to magnetic field lines.
    • (flux density, in teslas)
5Charge-to-mass ratio
  • Q/m, which determines the acceleration in a given field
6Field strength
  • G = Fg/m.

Key terms

TermMeaning
Magnetic flux densityThe force per unit current per unit length on a conductor at right angles to the field, measured in tesla.
TeslaThe flux density that gives a force of 1 N on 1 m of wire carrying 1 A at right angles to the field.
Velocity selectorAn arrangement of perpendicular electric and magnetic fields that passes only particles of speed E/B.
Left-hand ruleA rule giving the direction of the force on a current or positive charge moving in a magnetic field.
Permeability of free spaceThe constant μ0 = 4π × 10−7 N A−2.
Charge-to-mass ratioThe ratio of the total charge of a particle to its mass.

Avoid these mistakes

1
Using F = BIL for a single charge — use F = Bqv.
2
Forgetting to reverse the direction of the force for a negative charge.
3
Saying the magnetic force changes the speed of the particle — it only changes direction.
4
Using the left-hand rule with the electron flow direction instead of the conventional current.
5
Expecting a force when the current or velocity is parallel to the field.

Last updated:

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.