A circular loop of flexible iron wire has an initial circumference of 168cm , but its circumference is decreasing at a constant rate of 15.0cm/s due to a tangential pull on the wire. The loop is in a constant uniform magnetic field of magnitude 1.00T , which is oriented perpendicular to the plane of the loop. Assume that you are facing the loop and that the magnetic field points into the loop.

Question

A circular loop of flexible iron wire has an initial circumference of 168cm , but its circumference is decreasing at a constant rate of 15.0cm/s due to a tangential pull on the wire. The loop is in a constant uniform magnetic field of magnitude 1.00T , which is oriented perpendicular to the plane of the loop. Assume that you are facing the loop and that the magnetic field points into the loop.
Find the magnitude of the EMF induced in the loop after exactly time 9.00s has passed since the circumference of the loop started to decrease.

Elena · Answer

L2=L1- (ΔL/Δt) •t=168-135=33 cm
EMF=-dΦ/dt =- d(B•A•cosα)/ dt.
cosα=1.
L1=2•π•R1
R1=L1/2•π=168/2•3.14=26.7 cm
A1=π•R1²=3.14•26.7²=2246 cm²=0.2246 m²

L2=2•π•R2
R2=L2/2•π=33/2•3.14=2.25 cm
A2=π•R2²=3.14•2.25²=86.7 cm²=0.0087m²
EMF=-dΦ/dt =- d(B•A•cosα)/dt.
cosα=1.
EMF=-B•ΔA/Δt=
= -1•(0.2246-0.0087)/9=0.024 V