Forces on Conductors & Parallel Wires
Magnetic force on current-carrying conductors F = BIl sin θ, mutual force between parallel current-carrying wires F/l = (μ₀ I₁ I₂)/(2πd), attraction and repulsion criteria, the SI definition of the Ampere, and current balances.
Marking a lesson complete represents finishing your study of the topic; it does not denote tested mastery.
Learning Objectives
- Calculate the mechanical force on a straight current-carrying conductor in a magnetic field: F = B I l sin θ.
- Explain why parallel currents in the same direction attract and opposite currents repel, deriving force per unit length: F/l = (μ₀ I₁ I₂) / (2π d).
- State the historical and modern SI definitions of the Ampere and explain the operation of a current balance.
Core Theory & Concepts
Because an electric current is a macroscopic collective flow of mobile charges, placing a current-carrying wire in an external magnetic field causes each drifting charge to feel a microscopic Lorentz force. The sum of these microscopic forces manifests macroscopically as a powerful mechanical thrust on the wire.
Force on a Conductor
For a straight conductor of length l carrying current I in field B: F = B I l sin θ, directed via Fleming’s Left-Hand Rule.
Mutual Force Between Parallel Wires
Each wire creates a field B = (μ₀ I)/(2πd) at the other. Current in same direction produces attraction; opposite currents repel: F/l = (μ₀ I₁ I₂) / (2π d).
Common Misconceptions
Two parallel wires carrying currents in the same direction repel each other like two like electrostatic charges.
Syllabus Topic Outline
- 1Derivation of F = BIl sin θ from single-carrier Lorentz forces
- 2Action-reaction forces between two long parallel conductors
- 3Formula for force per unit length: F / l = (μ₀ I₁ I₂) / (2π d)
- 4Definition of the Ampere: historical 2 × 10⁻⁷ N m⁻¹ vs modern 2019 fixed elementary charge e
- 5The current balance experiment (Cotton balance) for measuring B