3.01 Fundamental Postulates of Magnetostatics & Lorentz Force Equation
Related Concepts: 2.01 Fundamental Postulates of Electrostatics & Gauss’s Law Applications | 3.02 Biot-Savart Law Applications (Finite Wire, Circular Loop, Coaxial Cable) | 3.03 Ampere’s Circuital Law & Vector Magnetic Potential (A)
3.01 Fundamental Postulates of Magnetostatics & Lorentz Force Equation
Overview: Magnetostatics is the study of steady (time-invariant) magnetic fields produced by constant direct currents (DC). The field behavior is anchored by two fundamental postulates: Conservation of Magnetic Flux (∇ · B = 0) and Ampere’s Curl Postulate (∇ × H = J).
1. Fundamental Postulates of Magnetostatics in Free Space [PYQ: 2015, 2016, 2018, 2021]
| Postulate Name | Differential (Point) Form | Integral Form | Physical Significance |
|---|---|---|---|
| Divergence Postulate | ∇ · B = 0 | ∮S B · ds = 0 | No Isolated Magnetic Monopoles: Magnetic flux lines always form continuous closed loops. |
| Curl Postulate | ∇ × H = J | ∮C H · dl = Ienclosed | Ampere’s Law: Circulation of magnetic field equals total enclosed free current. |
2. The Lorentz Force Equation [PYQ: 2018, 2021]
When a test charge q moves with velocity u in a region containing coexisting electric field E and magnetic field B, the total force experienced is the vector sum:
F = Fe + Fm = q(E + u × B) [Newtons]
2.1 Key Physical Features of Magnetic Force (Fm = qu × B)
1. Perpendicularity: Magnetic force Fm is always perpendicular to both charge velocity u and magnetic field B.
2. Zero Work Done: Because Fm · dl = q(u × B) · (u dt) = 0, a static magnetic field does no work on a moving charge; it alters particle direction but cannot change kinetic energy or speed.