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), parallel-wires zero-field point (2018).
- Ampère law and vector potential → — vector potential with the 2018 casework (three numerics), solenoid field $B = \mu_0 nI$ via Ampère’s law, 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 takes the wire field as input and proves Ampère’s circuital law from it — same physics, seen from the symmetry side. 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.