Questions
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 and density is d. The value of the induced current i is
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=m4πρddBdtSimilar Questions
An elasticized conducting band r is around a spherical balloon T (figure). Its plane passes through the center of the balloon. A uniform magnetic field of magnitude 0.04 T is directed perpendicular to the plane of the band. Air is let out of the balloon at 100 cm3s-1 at an instant when the radius of the balloon is 10 cm. The induced emf in the band is
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