A circular conducting hoop of wire has a constant

magnetic field |~B | = 1.7 Tesla passing through it so that the field direction is perpendicular to
the plane of the hoop. There is an EMF induced in the hoop with magnitude 2.6 Volts because
the hoops area A is shrinking (or equivalently the radius of the hoop is shrinking). What is the
magnitude of �A/�t which is the rate (in m2/s) at which the area is changing?

I forgot to add this part.

assume this wire has a resistance R which is a constant as the hoop is shrunk.
(a) What will be the current I which is
induced and show the direction of this current in your figure.

(b) What is the magnitude of the
induced B-field at the center of the hoop as a function of the radius R of the hoop? Show the
direction of the induced B-field.

To find the magnitude of �A/�t, we can use Faraday's law of electromagnetic induction, which states that the induced electromotive force (EMF) in a loop of wire is equal to the rate of change of magnetic flux through the loop. The magnetic flux, Φ, is given by the product of the magnetic field strength (|~B|) and the area (A) through which the magnetic field passes.

Mathematically, the equation for Faraday's law is:

EMF = -dΦ/dt

Where EMF is the induced electromotive force and dΦ/dt is the rate of change of magnetic flux.

In this case, the EMF is given as 2.6 Volts and the magnetic field strength is given as 1.7 Tesla. Since the magnetic field is perpendicular to the plane of the hoop, the magnetic flux through the hoop is constant.

Therefore, we can write:

EMF = -d(Φ)/dt = -|~B| * d(A)/dt

Substituting the given values:

2.6 = -1.7 * d(A)/dt

Now, we can solve for d(A)/dt:

d(A)/dt = 2.6 / (-1.7)

d(A)/dt = -1.529 m^2/s

So, the magnitude of �A/�t, which is the rate at which the area is changing, is 1.529 m^2/s.