AcademyMagnetic Fields and Forces
Academy
Magnetic Field Lines
Level 1 - Physics topic page in Magnetic Fields and Forces.
Principle
Magnetic field lines show field direction by tangent and field strength by density.
Notation
\(\vec B\)
magnetic field
\(\mathrm{T}\)
\(N\)
north pole label
\(S\)
south pole label
\(\Delta A\)
small area pierced by field lines
\(\mathrm{m^{2}}\)
Method
Field lines are a representation, not physical strings. They encode direction and relative magnitude.
Direction
\[\text{line tangent}\parallel\vec B\]
Relative strength
\[\text{larger line density}\rightarrow\text{larger }B\]
Closed loops
\[\text{magnetic field lines form closed curves}\]
Outside a bar magnet, field lines leave the north pole and enter the south pole. Inside the magnet, they continue from south to north to close the loops.
Rules
Tangent rule
\[\vec B\parallel\text{field-line tangent}\]
Flux idea
\[\Phi_B\sim B\Delta A\]
Closed-line rule
\[\nabla\cdot\vec B=0\]
Examples
Question
Where is a bar magnet's external field strongest in a field-line diagram?
Answer
Near the poles, where the field lines are most densely packed.
Checks
- Field lines never cross.
- Magnetic field lines form loops, unlike electrostatic field lines from isolated charges.
- Dense lines indicate large field magnitude, not larger particle speed.