When a circular foil of radius 1 m and 100 turns is rotated in a horizontal uniform magnetic filed t

Question

When a circular foil of radius 1 m and 100 turns is rotated in a horizontal uniform magnetic filed the peak value of e.m.f induced is 100 V . The coil is unwound and the rewound into a circular roil of radius 2 m . If it is rotated, now, with the same speed, under similar conditions, the new peak value of .f developed is\

Professor PC Thomas Classes · Answer

$\mathrm{V}_{\mathrm{m}}$ for a transformer $=2 \pi \mathrm{fNBA}=100 \mathrm{~V}$ Initial number of coils $\mathrm{N}=100$ and radius $=1 \mathrm{~m}$\ $	herefore 2 \pi \mathrm{f} 100 	imes \mathrm{B} \pi \mathrm{l}^{2}=100 \mathrm{~V}$\ Total length $=100 	imes 2 \pi 	imes 1=2 \pi 	imes 100=200 \pi \mathrm{~m}$\ The circumference of turn of radius $2 \mathrm{~m}=2 \pi 	imes 2 \mathrm{~m}$\ $	herefore$ No. of turns in $2 \pi 	imes 100 \mathrm{~m}$ is\ $\frac{2 \pi 	imes 100}{2 \pi 	imes 2}=50$ turns.\ $	herefore \mathrm{V}_{\mathrm{m}}=2 \pi 	imes \mathrm{f} 	imes 50 \mathrm{~B} 	imes \pi 	imes 2^{2}$\ $=2 \pi 	imes \mathrm{f} 	imes 50 \mathrm{~B} 	imes \pi .4$\ $\mathrm{V}_{\mathrm{m}}=2 \pi 	imes \mathrm{f} 	imes 50 \mathrm{~B} 	imes \pi 	imes 2^{2}=2 	imes 100=200 \mathrm{~V}$\