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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

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a
m2πρddBdt
b
m4πa2rdBdt
c
m4πaddBdt
d
m4πρddBdt

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detailed solution

Correct option is D

e=dϕdt⇒i=eR=1Rddt(BA)=ARdBdtwhere πr2= area of the loop of radius r and R = resistance of the loop of length 2πrand area of cross sectionπa2.R=ρlπa2=ρ2πrπa2Further mass of wire is m=πa22πrdi=πa2πr2ρ2πrdBdti=πa22πr4πρdBdt⇒i=m4πρddBdt

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