Magnetic Tension, Pressure, and Mechanical Balance
For a current element, dF = I dl cross B. In symmetric arc problems, local transverse load IB per unit length balances tension curvature T/R, giving T = IBR under the ideal flexible-wire assumptions.
Why this shows up in the exam
Tension in current-carrying arcs · Expansion or contraction of loops · Rods held against gravity on inclines
Learn the idea
Distributed magnetic force can create tension, expansion, contraction, or balance against weight. A wire or loop may not simply translate; magnetic force distributed along it can stretch an arc, expand a loop, or support a rod. Resolve local forces before applying mechanical equilibrium.
🧠 Memory hook: Magnetic force is a distributed load; balance it with the mechanical forces.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- dF = I(dl cross B) — distributed magnetic force on a current element
- force_per_length = I B — magnitude for a wire perpendicular to uniform B
- T = I B R — tension of an ideal circular flexible wire under uniform transverse magnetic loading
How to approach it
- 1Draw local magnetic-force directions
- 2Use symmetry to identify deformation or tension
- 3Apply force balance with weight, supports, or curvature
Common slip-ups that cost marks
- •Treating a curved wire as one straight segment for internal tension
- •Ignoring force direction around the loop
- •Using T = IBR outside the symmetric ideal case
🌟 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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