JEE/NEET Physics · Moving Charges & Magnetism series · Part 4 of 8 · All parts →
- Currents create magnetic fields — moving charge is magnetism’s source
- Biot-Savart: each wire bit contributes dB = (μ₀/4π)Idl×r̂/r² — an inverse-square weaver
- Long straight wire: B = μ₀I/(2πr) — circles around the wire
- Circular loop centre: B = μ₀I/(2R); solenoid interior: μ₀nI (uniform!)
- Right-hand grip rule: thumb along I, fingers curl along B
Oersted noticed a compass needle twitch beside a current-carrying wire in 1820 — the first hint that electricity and magnetism are family. Every current weaves a magnetic field around itself, and Biot-Savart’s law is the weaving pattern. Part 4 of the Moving Charges & Magnetism series.
- Oersted’s twitch
- The weaving law
- The straight wire’s circles
- Loops and solenoids
- Solved examples
- Common mistakes
- This physics in your daily life
- Practice set
- Recap
Oersted’s Twitch
Current on: nearby compass deflects. Current off: needle settles north. Electricity creates magnetism — no magnets needed, just moving charge. (It took so long to find because the effect is modest: μ₀/4π is a small constant.)
The Weaving Law
| Letter | What it means (plain words) | Value / unit |
|---|---|---|
| μ₀ | permeability of free space | 4π×10⁻⁷ T·m/A |
| dl | tiny length of wire, direction = current | m |
| r | distance from the element to the point | m — squared! |
The Straight Wire’s Circles
Integrate Biot-Savart along an infinite wire and the field is beautifully simple: B = μ₀I/(2πr) — concentric circles around the wire, following the right-hand grip rule (thumb = current, curled fingers = field direction).
Loops and Solenoids
| Source | Field | Shape |
|---|---|---|
| Long straight wire | μ₀I/(2πr) | circles |
| Loop centre | μ₀NI/(2R) | one strong uniform centre |
| Solenoid interior | μ₀nI (n = turns/m) | uniform, straight lines |
| Solenoid ends | ½μ₀nI | half the centre |
Solved Examples
B = (4π×10⁻⁷ × 5)/(2π × 0.1) = 10⁻⁵ T — about Earth-field scale: Oersted’s twitch explained.
✔
Answer: 10⁻⁵ T
B = μ₀NI/2R = (4π×10⁻⁷ × 100 × 0.5)/(0.1) ≈ 6.3×10⁻⁴ T.
✔
Answer: ≈0.63 mT
Solenoid: n = 1000 turns/m → B = μ₀nI ≈ 6.3×10⁻⁴ × (I/0.5)… at 0.5 A: 6.3×10⁻⁴ T — same order! But solenoids add field over a VOLUME, loops concentrate at a point.
The design lesson: geometry, not turn count alone, shapes fields.
✔
Answer: Comparable magnitudes, different geometry
- 1/r (wire) vs 1/r² (element). The single element falls as 1/r²; the integrated infinite wire as 1/r — know which you’re using.
- Wrong grip direction. Thumb is CURRENT; fingers are FIELD — reversing the assignment flips every answer’s direction.
- Solenoid n confusion. n = turns PER METRE, not total turns: 200 turns on 0.5 m is n = 400.
- Field inside materials. μ₀ is vacuum; iron cores multiply fields enormously (μᵣ) — the next series’ topic.
This Physics in Your Daily Life
- Every electromagnet ever — scrapyard cranes, relays, doorbells: current through coils weaving usable fields: Biot-Savart industrialised.
- MRI machines — superconducting solenoids weave 1.5–3 T fields with hundreds of amperes: medicine’s clearest images from a wire coil at 4 K.
- Magnetic shielding and transformers — field geometries designed by these formulas: the quiet hum of every adapter is woven field.
- Electric motors’ stators — deliberately shaped windings sculpt rotating fields: geometry of wire doing mechanical work.
- Wireless charging pads — loop fields coupling phone to charger: Biot-Savart’s circles transferring energy through air.
A wire carrying current is a river of marching charge — and Part 1 taught that magnetism is what electricity looks like when charge moves. The current IS moving charge en masse: of course it must have a magnetic signature. Each marching electron drags its little magnetic halo along, and the wire’s field is the sum of trillions.
5 A at 10 cm: 10⁻⁵ T — Earth-scale, why Oersted needed a delicate compass. The same 5 A wrapped into a tight 100-turn 5 cm coil: 600× stronger at the centre — geometry (concentrating circles) is a field multiplier more powerful than current itself.
Grip the wire with your right hand, thumb along the current: your fingers wrap in the field’s direction. The picture: nested circles around the wire like rings around a tree trunk, strength fading as 1/r outward.
Practice set (answers hidden — try first)
(NEET-level) B at 2 m from 10 A wire:
(JEE Main-level) Solenoid n = 500/m, I = 2 A: B ≈
(NEET-level) Doubling distance from a wire: B
(Concept) Magnetic field lines around a straight current form
(JEE Main-level) Field at a solenoid’s end vs centre:
- currents create fields (Oersted)
- Biot-Savart: element law, 1/r²
- wire: B = μ₀I/2πr (1/r, circles)
- loop: μ₀NI/2R; solenoid: μ₀nI
- right-hand grip rule
- 🔁 Biot-Savart structure
- 🔁 wire/loop/solenoid formulas
- 🔁 grip rule
- 🧠 Chant: ‘current in, circles out’.
- 🧠 Coils concentrate — turns buy field without amps.
- 🏠 Daily: scrapyard electromagnets = woven field.
- 🏠 Daily: wireless charging = loop fields in air.
Quick revision
- Currents create magnetic fields — moving charge is magnetism’s source
- Biot-Savart: each wire bit contributes dB = (μ₀/4π)Idl×r̂/r² — an inverse-square weaver
- Long straight wire: B = μ₀I/(2πr) — circles around the wire
- Circular loop centre: B = μ₀I/(2R); solenoid interior: μ₀nI (uniform!)
- Right-hand grip rule: thumb along I, fingers curl along B
- The straight wire’s circles
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