Definition of Magnetic Field on the Basis of Magnetic Force

Think of a compass needle near a live wire — it deflects because the current-carrying wire creates a magnetic field. Similarly, any moving charge experiences a force when placed in a magnetic field, and this deflecting force is precisely what lets us define and measure the magnetic field itself.

A region of space is said to have a magnetic field if a moving charged particle experiences a deflecting force in that region. This field is denoted by \[\vec{B}\] and is also called magnetic induction.

Step 1: Experimental Observation: A charge q moving with velocity v at an angle θ to a magnetic field experiences a deflecting force F.

Step 2: Proportionality Relations: Experiments show:

• F ∝ q
• F ∝ v
• F ∝ sin ⁡θ

Step 3: Combine into a Single Relation: F = Bqv sin⁡ θ

where B is the constant of proportionality — the magnetic field strength.

Step 4: Isolate B (Operational Definition): B = \[\frac {F}{qvsin⁡θ}\]

Step 5: Special Case Check: When θ = 0° or 180° (charge moves parallel/antiparallel to field): F = 0.

This means the magnetic field direction is the one along which a moving charge feels no magnetic force.