Why is force applied on a current-carrying conductor in an external magnetic field? Write its formula. What are the different factors on which this force depends? State the rule by which the direction of this force can be found.

The force applied on a current-carrying conductor in an external magnetic field arises due to the interaction between the magnetic field and the moving charged particles (electrons) in the conductor. When a current flows through a conductor, the electrons experience a force due to the magnetic field, which results in a net force on the entire conductor.

Formula for the force:

The force F on a current-carrying conductor in a magnetic field is given by:

F=BILsin⁡θ

Where:

  • = Force on the conductor (in newtons, N)
  • = Magnetic field strength (in teslas, T)
  • = Current flowing through the conductor (in amperes, A)
  • = Length of the conductor within the magnetic field (in meters, m)
  • θ = Angle between the direction of the magnetic field and the current in the conductor

Factors affecting the force:

The force depends on the following factors:

  1. Magnetic field strength (B): A stronger magnetic field results in a greater force.
  2. Current (I): A larger current generates a greater force, as the force is directly proportional to the current.
  3. Length of the conductor (L): The longer the conductor in the magnetic field, the greater the force.
  4. Angle (θ): The force is maximum when the magnetic field is perpendicular to the current (θ=90∘) and zero when the magnetic field is parallel to the current (θ=).

Direction of the force:

The direction of the force can be found using Fleming’s Left-Hand Rule. According to this rule:

  • Thumb: Represents the direction of the force (motion of the conductor).
  • First finger: Represents the direction of the magnetic field (from north to south).
  • Second finger: Represents the direction of the current (from positive to negative).

When you align your left hand with these directions, the thumb will point in the direction of the force experienced by the conductor.

This rule helps in determining how a current-carrying conductor will move when placed in a magnetic field, which is the fundamental principle behind electric motors.

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