A wire of $$cross-sectional$$ area A forms three sides of a square and is free to rotate about axis $$OO1$$. If the structure is deflected by an angle θ from the vertical when current I is passed through it in a magnetic field B acting vertically upward and density of the wire is ρ, then the value of θ is given by

Question

A wire of $$cross-sectional$$ area A forms three sides of a square and is free to rotate about axis $$OO1$$. If the structure is deflected by an angle θ from the vertical when current I is passed through it in a magnetic field B acting vertically upward and density of the wire is ρ, then the value of θ is given by

Infinity Learn · Accepted Answer

Let a is the side of square. Torque of current $$=MBsin(90-$$θ$$)$$ $$=MBcos$$θ$$=ia2Bcos$$θ  Mass of each side $$=m=$$ρAa  Torque of gravity $$=2mga2sin$$θ$$+mgasin$$θ $$=2mgasin$$θ$$=2$$ρ$$Aga2sin$$θ Now, both torques should be same  i.e.,   $$ia2Bcos$$θ$$=2$$ρ$$Aga2sin$$θ ⇒  $$cot$$θ$$=2$$ρAgiB

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