Magnetic Force 🤔
4.2.1 Sources and Fields
- Just like a charge Q creates an electric field \( \mathbf E \), a moving charge (or current) produces a magnetic field \( \mathbf B \) 🧲:contentReference[oaicite:0]{index=0}.
- Both fields are vectors defined at every point in space and obey the superposition principle—add them tip-to-tail to find the net field 💡:contentReference[oaicite:1]{index=1}.
- Conventions for direction: a dot (•) shows field or current coming out of the page, a cross (×) shows it going into the page ➡️:contentReference[oaicite:2]{index=2}.
4.2.2 Magnetic Field & Lorentz Force
The total force on a charge q moving with velocity \( \mathbf v \) in electric and magnetic fields is
\( \displaystyle \mathbf F = q\,[\,\mathbf E + \mathbf v \times \mathbf B\,] \) 🎯:contentReference[oaicite:3]{index=3}
- The magnetic part \( q\,\mathbf v \times \mathbf B \) acts only when the charge moves (no motion ⇒ no magnetic force) and is always perpendicular to both \( \mathbf v \) and \( \mathbf B \) 🏄♂️:contentReference[oaicite:4]{index=4}.
- Right-hand rule 👍: point fingers along \( \mathbf v \), curl toward \( \mathbf B \); the thumb shows the force direction for a positive charge (reverse for negative) :contentReference[oaicite:5]{index=5}.
- If \( \mathbf v \parallel \mathbf B \) or the charge is at rest, the magnetic force is zero ✨:contentReference[oaicite:6]{index=6}.
How big is one tesla?
Set q = 1 C, | \( \mathbf v \) | = 1 m s-1, and magnetic force F = 1 N acting perpendicular to the velocity; the required field is 1 T. A smaller non-SI unit often used is the gauss (\( 1\,\text{G} = 10^{-4}\,\text{T} \)). The Earth’s field is only about \( 3.6\times10^{-5}\,\text{T} \) 🌏:contentReference[oaicite:7]{index=7}.
4.2.3 Magnetic Force on a Current-Carrying Conductor
For a straight segment of wire of length vector \( \mathbf l \) (direction ➡️ current) that carries current I in an external field \( \mathbf B \),
\( \displaystyle \mathbf F = I\,\mathbf l \times \mathbf B \) ⚡:contentReference[oaicite:8]{index=8}
- The same right-hand rule gives the direction.🙌
- If the wire is shaped arbitrarily, sum (integrate) tiny elements \( I\,d\mathbf l \times \mathbf B \).:contentReference[oaicite:9]{index=9}
Quick check-in example 🎓
A 1.5 m wire of mass 0.2 kg carrying 2 A can “float” in a horizontal field of \( 0.65\,\text{T} \) because the upward magnetic force \( I l B \) balances its weight \( mg \) 💪:contentReference[oaicite:10]{index=10}.
High-Yield Ideas for NEET 🏆
- \( \mathbf F = q(\mathbf E + \mathbf v \times \mathbf B) \) — know the three vectors’ mutual right-angle relationship thoroughly.💯
- Zero magnetic force situations: stationary charges or motion exactly along/against \( \mathbf B \).🔍
- Unit of field (tesla) defined with a 1 C charge moving at 1 m s-1 experiencing 1 N — easy marks!📏
- Wire force formula \( \mathbf F = I\,\mathbf l \times \mathbf B \) and its use in balance problems (e.g., levitating wire).🧮
- Dot (•) / cross (×) pictograms for field or current directions — frequently tested in diagrams.🖼️
Keep practicing right-hand rules—muscle memory today means free marks tomorrow! 🚀
