By S. Hussain Ather • Updated Aug 30, 2022
Magnets sometimes push each other away and at other times pull together. Understanding the subtle physics that governs this behavior is essential for everything from electric motors to medical imaging devices.
Like electric charges, magnetic poles come in two kinds: north (N) and south (S). A north pole always attracts a south pole, while two north poles or two south poles repel each other. This simple rule underlies the operation of compasses, magnetic bearings, and many industrial applications.
When charged particles move, they generate magnetic fields that exert forces on other moving charges. The Biot–Savart law quantifies this interaction:
F = \frac{\mu_0 q_1 q_2}{4\pi |r|^2} \; v_1 \times (v_2 \times r)
Here, μ₀ = 12.57×10⁻⁷ H/m is the vacuum permeability, q₁ and q₂ are the charges, v₁ and v₂ their velocities, and r the separation vector. The cross product indicates that the force depends on the relative directions of motion and separation.
Unlike electric forces, magnetic forces only act on moving charges and never on static magnetic monopoles—particles that would possess only one magnetic pole. No experimental evidence for such monopoles has yet been found.
The sign of the cross product determines whether two moving charges attract or repel. If the resulting force vectors point toward each other, the charges attract; if they point away, the charges repel. The same principle applies to macroscopic magnets: the orientation of their magnetic moments dictates whether they push or pull.
Current in a wire produces a magnetic field that can be visualized with the right‑hand rule. Point your thumb in the direction of the conventional current; your curled fingers show the field direction. Two parallel wires carrying currents in the same direction attract, while currents in opposite directions repel—an effect exploited in electromagnets and magnetic levitation.
The Lorentz force law extends this idea to charged particles moving through external fields:
F = qE + qv \times B
where E is the electric field, B the magnetic field, and v the particle’s velocity. The cross product again determines the direction of the magnetic component.
Every magnet behaves like a tiny dipole with a magnetic moment m. When placed in an external field B, it experiences a torque:
τ = m \times B = |m||B|\sin\theta
That torque aligns the dipole with the field, as seen in a compass needle pointing toward geographic north. The potential energy of a dipole in a field is U = -m\cdot B = -|m||B|\cos\theta, reaching a minimum when the dipole aligns with the field.
Atoms with unpaired electrons (paramagnets) are attracted to magnetic fields, while atoms with all paired electrons (diamagnetics) are repelled. Oxygen gas (O₂) is paramagnetic, whereas nitrogen gas (N₂) is diamagnetic. The behavior stems from the interaction of atomic magnetic dipoles with external fields.
When a strong neodymium magnet is moved along a steel screwdriver, the screwdriver becomes temporarily magnetized. Removing the magnet leaves a residual magnetism—a real‑world illustration of magnetic induction and the attractive force between aligned dipoles.
Understanding these principles equips engineers and scientists to design more efficient motors, secure magnetic bearings, and advanced medical imaging systems.
