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Torque on Coils

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Exercise

https://texercises.com/exercise/torque-on-coils/

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Exercise:
A square coil and a rectangular coil are each made from the same length of wire. Each contains a single turn. The long sides of the rectangle are twice as long as the short sides. Find the ratio ssctausquare:ssctaurectangle of the maximum torques that these coils experience in the same magnetic field when they contain the same current.

Solution:
Let a be the length of the short sides of the rectangle. The long sides are then b a and the wire has a length of L a+ b a+ a a The area of the rectangular coil is sscArectangle a b a a a^ The square has sides with length a' fracL frac a frac a Its area is sscAsquare a'^ leftfrac aright^ frac a^ The maximum torque on a coil in a magnetic field is given by tau I A B We thus find fracssctausquaressctaurectangle fracsscAsquaresscArectangle frac/ a^ a^ frac

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Branches	Magnetism
Tags	biot-savart, magnetic force, torque
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Difficulty	(2, default)
Points	0 (default)
Language	(English)
Type	Calculative / Quantity
Creator	by
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