The magnetic flux density B is changing in magnitude at a constant rate $$dB/dt$$. A given mass m of copper, drawn into a wire of radius a and formed into a circular loop of radius r is placed perpendicular to the field B. The induced current in the loop is i. The resistivity of copper is ρ and density is d. The value of the induced current i is

Question

The magnetic flux density B is changing in magnitude at a constant rate $$dB/dt$$. A given mass m of copper, drawn into a wire of radius a and formed into a circular loop of radius r is placed perpendicular to the field B. The induced current in the loop is i. The resistivity of copper is ρ and density is d. The value of the induced current i is

Infinity Learn · Accepted Answer

$$e=d$$ϕdt⇒$$i=eR=1Rddt(BA)=ARdBdtwhere$$ π$$r2=$$ area of the loop of radius r and R $$=$$ resistance of the loop of length $$2$$$$π$$rand area of cross section$$π$$$$a2$$.$$R=$$ρl$$π$$$$a2=$$ρ$$2$$$$π$$r$$π$$$$a2Further$$ mass of wire is $$m=$$π$$a22$$$$π$$$$rdi=$$π$$a2$$$$π$$$$r2$$ρ$$2$$$$π$$$$rdBdti=$$π$$a22$$$$π$$$$r4$$πρdBdt⇒$$i=m4$$πρddBdt

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