Question

A circular loop of flexible iron wire has an initial circumference of 165.0 cm, but its circumference is decreasing at a constant rate of 12.0 cm>s due to a tangential pull on the wire. The loop is in a constant, uniform magnetic field oriented perpendicular to the plane of the loop and with magnitude 0.500 T. (a) Find the emf induced in the

Answer 1

emf = - 0.622 V

Step-by-step explanation:

The electromotive force is given by Faraday's law

emf =
`- (d \phi )/(dt)`

Ф = B. A

bold indicates vectors

Ф = B A cos θ

in this case it is indicated that the magnetic field is constant and the angle between the magnetic field and the normal to the area is parallel, so the cos 0 = 1

we substitute

emf =
`- B \ (dA)/(dt)`

the area of ​​the circle is

A = pi r²

`(dA)/(dt) = \pi 2r \ (dr)/(dt)`

emf = B 2π r
`(dr)/(dt)`

speed is defined

v =
`(dr)/(dt)`

we substitute

emf = - 2π B r v

let's calculate

emf = - 2π 0.5 1.65 π0.12

emf = - 0.622 V