Force On A Moving Charge (Copy)

Magnetic Force on a Moving Charge

• A charged particle (q) moving with velocity v in a magnetic field (B) experiences a force (F) given by:

  F = Bqv sin θ

  Where:

  • F = Magnetic force (N)
  • B = Magnetic flux density (T)
  • q = Charge (C)
  • v = Velocity of the particle (m/s)
  • θ = Angle between v and B
• Maximum force occurs when θ = 90°
• No force when the motion is parallel or antiparallel to the field (θ = 0° or 180°)

Direction of Force – Fleming’s Left-Hand Rule

• Apply the same rule as used for current-carrying conductors:
  • Thumb → Direction of Force (F)
  • First Finger → Direction of Field (B)
  • Second Finger → Direction of Current (or velocity of positive charge)
• For negative charges (e.g. electrons), reverse the direction of current (velocity)

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course

Motion in a Uniform Magnetic Field

• When a charged particle enters a uniform magnetic field perpendicular to its velocity:
  • It experiences a centripetal force due to the magnetic force
  • It undergoes circular motion
• Equating magnetic force to centripetal force:

  Bqv = mv² / r

  Rearranged:

  r = mv / (Bq)

  Where:

  • r = Radius of the circular path
  • m = Mass of particle
  • v = Speed of particle
  • B = Magnetic flux density
  • q = Charge of particle
• The angular frequency (cyclotron frequency) of rotation is:

  f = Bq / (2πm)

• The motion is circular (if θ = 90°) or helical (if θ ≠ 90°)

Hall Effect and Hall Voltage

• When a current-carrying conductor or semiconductor is placed in a magnetic field:
  • Charge carriers experience a magnetic force
  • They are pushed to one side, creating a potential difference
  • This voltage is called the Hall voltage (Vᴴ)
• Hall voltage formula:

  Vᴴ = BI / (ntq)

  Where:

  • B = Magnetic flux density (T)
  • I = Current (A)
  • n = Charge carrier density (number of charge carriers per unit volume)
  • t = Thickness of the conductor (m)
  • q = Charge of the carrier (C)
• This equation is derived by balancing:
  • Magnetic force: F = Bqv
  • Electric force: F = qE = q(Vᴴ / w)
• The Hall voltage gives direct measurement of magnetic field strength

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course

Applications of the Hall Effect

• Hall probe: Measures magnetic flux density B
• Semiconductor characterisation: Determine charge carrier density (n) and type of carrier (electron or hole)
• Automotive sensors, current sensors, and non-contact position sensing

Velocity Selection Using Electric and Magnetic Fields

• Velocity selector uses:
  • Electric field E creating a force F = qE
  • Magnetic field B creating a force F = Bqv
• In velocity selector:
  • Fields are set perpendicular and adjusted such that:

    qE = Bqv

  • Cancelling q:

    v = E / B

• Only particles with velocity v = E / B pass through undeflected

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course

Summary Table

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change A2 Level Physics Full Scale Course