Bar Magnet 🧲 — Quick, Friendly Notes
1. Meet the Bar Magnet
A bar magnet has two poles: North and South. Bring unlike poles together and they attract; like poles repel. Break the magnet in half and—surprise!—you simply get two weaker bar magnets, each still with a North and a South pole. No isolated “magnetic charges” (monopoles) pop out. 🧩:contentReference[oaicite:0]{index=0}
2. Drawing the Invisible: Magnetic Field Lines ✨
- Field lines form closed loops—they never start or end in space. Think of them as elastic bands stretching from the North pole around to the South pole and back inside the magnet.🌀
- The tangent to a line gives the direction of the magnetic field \( \mathbf{B} \) at that point.
- The closer the lines, the stronger the field (denser = stronger). 💪
- Lines never cross—otherwise the field would point two ways at once, which can’t happen.
One fun way to see them is sprinkling iron filings on a sheet over the magnet; the filings line up along the field. 🌾:contentReference[oaicite:1]{index=1}
3. Bar Magnet ≈ Solenoid (Coils of Current)
A long, current-carrying solenoid creates a field pattern almost identical to a bar magnet. Ampère’s cool idea: imagine a magnet as countless tiny circulating currents. ✨:contentReference[oaicite:2]{index=2}
Far from either device, the axial magnetic field looks like \( B = \dfrac{\mu_0}{4\pi}\dfrac{2m}{r^{3}} \) (5.1), where \( m \) is the magnetic moment and \( r \) the distance from the centre.:contentReference[oaicite:3]{index=3}
4. A Tiny Dipole in a Uniform Field 🎯
Place a little magnetic needle (moment \( \mathbf{m} \)) in a uniform field \( \mathbf{B} \). It feels a torque \( \boldsymbol{\tau} = \mathbf{m} \times \mathbf{B} \) (5.2), with magnitude \( \tau = mB\sin\theta \). The potential energy is \( U = -\mathbf{m}\!\cdot\!\mathbf{B} \) (5.3)—lowest when the needle lines up with the field (stable) and highest when anti-aligned (unstable).⚖️:contentReference[oaicite:4]{index=4}
5. Quick Electrostatic Analogy ⚡
Swap symbols in electric-dipole formulas and you instantly get the magnetic versions:
| Electric Dipole | Magnetic Dipole |
|---|---|
| Permittivity \( \dfrac{1}{\varepsilon_0} \) | Permeability \( \mu_0 \) |
| Dipole moment \( \mathbf{p} \) | Dipole moment \( \mathbf{m} \) |
| Axial field \( \dfrac{2p}{4\pi\varepsilon_0 r^{3}} \) | Axial field \( \dfrac{2\mu_0 m}{4\pi r^{3}} \) |
| Equatorial field \( -\dfrac{p}{4\pi\varepsilon_0 r^{3}} \) | Equatorial field \( -\dfrac{\mu_0 m}{4\pi r^{3}} \) |
| Torque \( \mathbf{p}\times\mathbf{E} \) | Torque \( \mathbf{m}\times\mathbf{B} \) |
| Energy \( -\mathbf{p}\!\cdot\!\mathbf{E} \) | Energy \( -\mathbf{m}\!\cdot\!\mathbf{B} \) |
Handy 💡 for converting one world into the other!:contentReference[oaicite:5]{index=5}
6. Gauss’s Law for Magnetism 🌐
Take any closed surface—any shape you like. Count magnetic field lines going out and in. They balance exactly, so the net magnetic flux is zero: \( \displaystyle \sum \mathbf{B}\!\cdot\!\Delta\mathbf{S} = 0 \). In short, no magnetic “charge” lives inside. 🧳:contentReference[oaicite:6]{index=6}
7. High-Yield NEET Nuggets 🥇
- Field-line properties: closed loops, density ↔ strength, never intersect.
- Axial and equatorial field formulas: remember the \( 2 \) vs \( -1 \) factors.
- Torque and potential energy of a dipole in a uniform field.
- No magnetic monopoles: cutting a magnet always yields smaller dipoles.
- Gauss’s magnetic law: zero net flux through any closed surface.
8. Tiny Quiz Corner 🤔
- If you halve a solenoid’s current, what happens to its magnetic moment?
- Which orientation of a dipole in a uniform field has the highest potential energy?
- Why can’t magnetic field lines start or end at a point in space?
Keep exploring, and happy magnetism adventures! 🚀
