Force on a Shaped Wire in Uniform Field
With constant current I and uniform B, F = I integral(dl cross B) = I(L_end-to-end cross B). For a closed loop in uniform B, the endpoint displacement is zero, so net force is zero.
Why this shows up in the exam
Forces on triangular or curved wire pieces · Quick net-force evaluation for bent conductors · Recognizing zero net force on closed loops
Learn the idea
For any open wire in uniform B, the net force depends only on the endpoint displacement, not the detailed shape. Tiny pieces of a bent wire each feel a force. In a uniform field their vector sum collapses to the straight displacement from the starting endpoint to the ending endpoint.
🧠 Memory hook: Uniform field sees endpoints for force, but shape can still matter for torque.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- F = I integral(dl cross B) — force on an arbitrary current path
- F = I(L_end-to-end cross B) — uniform-field endpoint result
- F_closed_loop = 0 — net force on a closed loop in uniform B
How to approach it
- 1Check that B is uniform
- 2Replace the path by its endpoint vector
- 3Use the cross product and separately examine torque if asked
Common slip-ups that cost marks
- •Using arc length instead of endpoint displacement
- •Concluding every closed loop has zero torque
- •Applying the endpoint shortcut in a nonuniform field
🌟 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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