Magnetic Field Lines and Absence of Monopoles
Gauss's law for magnetism states that net magnetic flux through every closed surface is zero: closed integral B dot dA = 0. Equivalently, div B = 0, so magnetic field lines have no sources or sinks.
Why this shows up in the exam
Choosing valid bar-magnet field diagrams · Testing whether a closed-loop drawing can represent a field · Reasoning about broken magnets
Learn the idea
Magnetic field lines form closed loops because isolated magnetic poles have not been observed. Cutting a bar magnet never leaves one north pole and one south pole; each piece becomes a smaller dipole. Field lines therefore continue through the magnet and outside it instead of beginning or ending at isolated magnetic charge.
🧠 Memory hook: Magnetic lines loop; they do not start or stop.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- closed integral B dot dA = 0 — zero net magnetic flux through any closed surface
- div B = 0 — local statement of no magnetic monopole source
- field lines never intersect — B has one direction at each ordinary point
How to approach it
- 1Check that every line closes
- 2Check outside direction north to south and inside south to north
- 3Reject intersections, starts, or ends in empty space
Common slip-ups that cost marks
- •Drawing field lines from north to south both inside and outside the magnet
- •Treating zero net flux as zero field everywhere
- •Allowing field lines to cross
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A charge of 2 microC moves perpendicular to a 3 T magnetic field at 4 x 10^5 m/s. Find the magnetic force.
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