Magnetic Fields Due To Currents (Copy)

Magnetic Field Due to a Long Straight Wire

• A current-carrying wire generates a circular magnetic field around it.
• Use the Right-hand thumb rule:
  • Thumb → direction of current
  • Curled fingers → direction of magnetic field
• Field strength around a straight wire at distance r:

  B = μ₀I / (2πr)

  Where:

  • B = magnetic flux density (T)
  • μ₀ = permeability of free space = 4π × 10⁻⁷ H/m
  • I = current (A)
  • r = radial distance from the wire (m)
• Magnetic field lines:
  • Concentric circles
  • Closer spacing = stronger field

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

Magnetic Field Due to a Flat Circular Coil

• Magnetic field lines:
  • Circular loops around each wire segment
  • At the center of the coil: magnetic field is strong and uniform
  • The direction is found using the Right-hand grip rule:
    • Fingers follow current around the loop
    • Thumb gives direction of the magnetic field at the center
• Field at center of single circular loop:

  B = μ₀I / (2r)

• For N loops (turns):

  B = Nμ₀I / (2r)

Magnetic Field Due to a Long Solenoid

• A solenoid is a long coil of wire, with many closely spaced turns.
• Magnetic field inside a solenoid is:
  • Uniform and strong
  • Parallel field lines
  • Direction found using Right-hand grip rule:
    • Fingers curl in the direction of current
    • Thumb points in the direction of field inside solenoid
• Field strength:

  B = μ₀nI

  Where:

  • n = number of turns per unit length (turns/m)
  • I = current (A)

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

Effect of Ferrous Core in Solenoid

• Inserting a ferrous (iron) core in a solenoid:
  • Increases magnetic field strength
  • The core becomes magnetized by induced field
  • Acts as a magnetic amplifier
  • Converts the solenoid into an electromagnet
• Field becomes much stronger and concentrated

Force Between Current-Carrying Conductors

• Two parallel conductors carrying currents exert forces on each other due to magnetic fields.

When currents are in the same direction:

• Wires attract each other

When currents are in opposite directions:

• Wires repel each other
• This interaction forms the basis for the definition of the ampere.

Force per unit length between two parallel wires:

F / L = μ₀I₁I₂ / (2πd)

Where:

• F = force (N)
• L = length of conductor (m)
• I₁, I₂ = currents in the wires (A)
• d = separation between wires (m)

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