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Asked in AIPMT 2011 · Force on a wire in a field
Given: a closed triangular loop in a uniform field that lies along the side AB.
Idea: the total force on a closed loop in a uniform field is zero, so work out which arms contribute and let the rest follow.
Arm AB: the current there runs along ⃗B, so d⃗l×⃗B=0 and the force on AB is zero.
The three forces must sum to zero: ⃗F_AB+⃗F_BC+⃗F_CA=0.
With ⃗F_AB=0, that leaves ⃗F_BC+⃗F_CA=0.
⃗F_CA=-⃗F.
The extra length of the hypotenuse is exactly offset by the smaller angle it makes with ⃗B.
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