Force On A Current-Carrying Conductor (Copy)

Force on a Current-Carrying Conductor in a Magnetic Field

• When a conductor carrying current (I) is placed in a magnetic field (B), it experiences a force (F).
• This is due to the interaction between:
  • The magnetic field
  • The moving charges (electrons) inside the conductor
• This force is called the motor effect.

Mathematical Expression for Force

• The magnitude of the force is given by the formula:

  F = BIL sin θ

  Where:

  • F = Magnetic force on conductor (in newtons, N)
  • B = Magnetic flux density (in tesla, T)
  • I = Current in the conductor (in amperes, A)
  • L = Length of the conductor within the magnetic field (in metres, m)
  • θ = Angle between the conductor and the magnetic field
• Special case:
  • If the conductor is perpendicular to the magnetic field, then θ = 90° and sin θ = 1
  • So the formula simplifies to:
    F = BIL

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

Direction of Force – Fleming’s Left-Hand Rule

• The direction of the force is determined using:

  Fleming’s Left-Hand Rule:

  • Thumb → Direction of Force (F)
  • First Finger → Direction of Field (B) (North to South)
  • Second Finger → Direction of Current (I) (Positive to Negative)
• All three must be held at right angles to each other.

Example: Using the Left-Hand Rule

• A wire is placed in a uniform magnetic field pointing from left to right.
• If current flows upwards through the wire:
  • Field = left to right (First finger)
  • Current = upward (Second finger)
  • Then the force = out of the page (Thumb)

Definition of Magnetic Flux Density (B)

• Magnetic flux density is defined as:
  

  The force per unit current per unit length acting on a conductor placed perpendicularly in a magnetic field.

• Mathematically, when θ = 90°:

  B = F / (IL)

  Units:

  • B: Tesla (T)
  • 1 Tesla = 1 newton per ampere per metre
    i.e. 1 T = 1 N A⁻¹ m⁻¹

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

Physical Meaning of B

• Magnetic flux density (B) measures how strong a magnetic field is.
• A magnetic field of 1 T will exert a force of 1 newton on a wire:
  • 1 m long,
  • carrying 1 A current,
  • placed perpendicular to the field.

Applications of the Motor Effect

• Electric motors: Use this principle to create rotational motion.
• Loudspeakers: Use forces on a wire in a magnetic field to create sound.
• Railguns and linear accelerators: Use magnetic forces to accelerate objects.

Graphical Interpretation

• F vs sin θ graph:
  • A sine curve with maximum value at θ = 90°
• F vs θ:
  • Shows the force is maximum when the wire is perpendicular (sin θ = 1)
  • Force is zero when wire is parallel to the field (θ = 0° or 180°)

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

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