Finite Bar Magnets, Shape, and Magnetic Length
In the pole model, magnetic moment m = p_m times 2l_m, where p_m is pole strength and 2l_m is magnetic length. For a thin strip bent without changing pole strength, the new moment scales with the straight-line separation of its ends.
Why this shows up in the exam
Bent magnetic strips · Finite-bar field and geometry questions · Uncertainty propagation in magnet formulas
Learn the idea
A finite magnet's moment equals pole strength times magnetic length, so reshaping changes pole separation. The material and pole strength may remain the same while bending a magnet brings its poles closer. Its magnetic moment then changes because the effective separation between poles changes.
🧠 Memory hook: Same poles, new separation, new moment.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- m = p_m (2 l_m) — bar-magnet moment in the pole model
- m_new/m_old = end_separation_new/end_separation_old — shape-change relation when pole strength is unchanged
- delta y/y = |n| delta x/x for y proportional to xⁿ — first-order relative-uncertainty propagation
How to approach it
- 1Decide whether the short-dipole or finite-magnet model applies
- 2Identify the effective pole separation
- 3For uncertainty, logarithmically differentiate the actual expression
Common slip-ups that cost marks
- •Using arc length as pole separation after bending
- •Assuming magnetic moment is unchanged for every shape change
- •Adding percentage uncertainties without using powers in the formula
🌟 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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