Interactive LearningWare 22.2 at wiley/college/cutnell reviews the fundamental approach in problems such as this. A constant magnetic field passes through a single rectangular loop whose dimensions are 0.35 m 0.55 m. The magnetic field has a magnitude of 2.1 T and is inclined at an angle of 75° with respect to the normal to the plane of the loop.


(a) If the magnetic field decreases to zero in a time of 0.46 s, what is the magnitude of the average emf induced in the loop?
V
(b) If the magnetic field remains constant at its initial value of 2.1 T, what is the magnitude of the rate A / t at which the area should change so that the average emf has the same magnitude as in part (a)?
m2/s

Please tell me where I went wrong.

This is what I did but it is incorrect.

a.

initial Phi= 75 degrees
= (2.1T)(0.1925 m^2)(cos 75 degrees)
= 0.104627

Final Phi= 0 degrees
= (2.1T)(0.1925 m^2)(cos 0 degrees)
= 0.40425

delta Phi = 0.104627 - 0.40425
= -0.299622401

E= -N (delta Phi/delta t)
E= -1(-0.299622401/0.46 s)
E= 0.651353046 V

Can you please explain part b.

I am wondering what äverage'means here. If it is really average, then you would have to integrate over time, and divide by the time.

Please clarify.

To solve part (b), you need to find the rate of change of the area, denoted as A/t, so that the average emf has the same magnitude as in part (a).

In part (a), you found that the average emf induced in the loop is 0.651353046 V. This average emf is directly proportional to the rate of change of magnetic flux through the loop, which is the product of the magnetic field and the rate of change of the area:

emf = -(dΦ/dt)

Here, emf is the average emf induced in the loop, dΦ/dt is the rate of change of magnetic flux, and the negative sign indicates the direction of induced current in accordance with Faraday's law.

In this case, the magnetic field remains constant at its initial value of 2.1 T. So, you need to solve for A/t, the rate at which the area should change to generate the same average emf.

From part (a), you obtained the average emf as 0.651353046 V. Now, you can rearrange the equation to solve for A/t:

emf = -(dΦ/dt) = -(B * dA/dt)

Rearranging, we have:

dA/dt = -emf / B

Plugging in the previously calculated values:

dA/dt = -0.651353046 V / 2.1 T

Simplifying, you will get the magnitude of the rate A/t in units of m²/s.