A current carrying loop is in the shape of an equilateral triangle of side length a. It's mass is M and it is in vertical plane. There exists a uniform horizontal magnetic field B→ of magnitude $$B0$$ in the region (up$$ to dotted $$line) as shown in the diagram. (neglect$$ emf induced in the $$loop)

Question

A current carrying loop is in the shape of an equilateral triangle of side length a. It's mass is M and it is in vertical plane. There exists a uniform horizontal magnetic field  B→ of magnitude  $$B0$$ in the region (up$$ to dotted $$line) as shown in the diagram. (neglect$$ emf induced in the $$loop)

Infinity Learn · Accepted Answer

Effective length of loop DABE is line joining DE.ℓ$$e=2ytan$$⁡$$30$$∘$$=2y3If$$ $$y=3a4then$$ ℓ$$e=23$$×$$3a4=a2$$ At equilibrium iℓ$$eB0=Mg$$⇒$$i=2MgaB0$$ When it is displaced slightly : $$dF=iB0d$$ℓ$$=$$−$$2MgaB0$$×$$B0$$×$$23dy=$$−$$4Mg3adyMa=$$−$$4Mg3adycomparing$$ with angular SHM $$a=-$$ω$$2y$$ω$$2=4g3a$$⇒$$2$$$$π$$$$T=4g3a$$∴$$T=2$$$$π$$$$3a4g$$

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A current carrying loop is in the shape of an equilateral triangle of side length a. It's mass is M and it is in vertical plane. There exists a uniform horizontal magnetic field B→ of magnitude B0 in the region (up to dotted line) as shown in the diagram. (neglect emf induced in the loop)

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