An α−particle and a proton are moving in circular paths in the same uniform magnetic field with same kinetic energy. Then the ratio of magnetic moment due to the rotation of α−particle to that of proton is

Question

An α−particle and a proton are moving in circular paths in the same uniform magnetic field with same kinetic energy. Then the ratio of magnetic moment due to the rotation of α−particle to that of proton is

Infinity Learn · Accepted Answer

$$(4)12$$ $$mv2=K$$.E.$$=E$$   ⇒ $$v=2EmAngular$$  velocity ω$$=QBm$$∴   $$r=Radius$$  of  circular  $$path=v$$ω$$=mQB$$.  $$2Em$$ $$=$$ $$2mE1QBi$$ $$=$$ Equivalent current due to the moving charge.$$=Q$$ω$$2$$π$$=Q2B2$$$$π$$m∴  $$M=Magnetic$$  dipole  moment  $$=$$π$$r2$$ ×  $$i=$$π×$$2EmQ2B2$$×  $$Q2B2$$$$π$$m⇒   $$M=EB$$∴      MαMρ$$=1$$

An $α - p a r t i c l e$ and a proton are moving in circular paths in the same uniform magnetic field with same kinetic energy. Then the ratio of magnetic moment due to the rotation of $α - p a r t i c l e$ to that of proton is

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