Magnetostatics is the study of steady currents and the steady magnetic fields they produce. The two tools that solve every exam question here are Biot–Savart law (build up a field from small current pieces) and Ampère law (read off a field using symmetry). One key constant appears everywhere: $\mu_0 = 4\pi \times 10^{-7}$ H/m.
Subpages
- Biot–Savart: wire and loop → — state the law (×3), straight-wire derivation with the 2023 numeric ($I=1.5$ A, $r=3$ cm → $B=10,\mu$T), loop-axis derivation (×2).
- Ampère law and vector potential → — vector potential with the 2018 casework, Ampère law and $\nabla\times\vec{B}=\mu_0\vec{J}$ (×3), meaning and proof of $\nabla\cdot\vec{B}=0$ (2022).
Most-repeated questions
- Biot–Savart statement — 2018, 2019, 2022 (×3).
- Ampère circuital law / $\nabla\times\vec{B}=\mu_0\vec{J}$ — 2018, 2019, 2023 (×3).
- Field of a long straight wire — 2019, 2022, 2023 (×3).
- Magnetic vector potential (with $\vec{B}=\nabla\times\vec{A}$) — 2018, 2022 (×2).
- Field on the axis of a circular loop — 2018, 2023 (×2).
How to use
Read the Biot–Savart page first. It gives you the wire and loop results by direct integration. Then read the Ampère page. It re-derives the same wire field in two lines using the symmetry of an infinite wire. Same answer, easier algebra — examiners love seeing both methods.
Reference. Brij Lal & Subrahmanyam Ch-7, 8; H.C. Verma Vol-1 Ch-35; S.L. Arora Vol-1 Ch-4.