An emf is induced in a conducting loop of wire 1.24 m long as its shape is changed from square to circular. Calculate the average magnitude of the induced emf if the change in shape occurs in 4.21 s, and the local 0.123 T magnetic field is perpendicular to the plane of the loop.

Emf = d(Flux)/dt

In this case, the area changes but B stays the same.
d(Flux)dt = B*d(Area)/dt

The area change is d(Area) = (circle area - square area)

To calculate the average magnitude of the induced emf, we can use Faraday's Law of electromagnetic induction which states that the emf (ε) induced in a conducting loop is directly proportional to the rate of change of magnetic flux through the loop.

The formula for the average magnitude of the induced emf is given by:

ε = (ΔΦ/Δt)

Where:
ε = average magnitude of the induced emf
ΔΦ = change in magnetic flux
Δt = change in time

To calculate the change in magnetic flux, we need to find the initial and final magnetic flux through the loop.

For the initial square shape, the magnetic flux through the loop (Φ_initial) is given by:

Φ_initial = B * A_initial

Where:
B = magnetic field strength (0.123 T)
A_initial = area of the initial square loop (side length squared)

Since the loop is 1.24 m long, the initial square loop has a side length of 1.24 m. Hence, the initial area (A_initial) is given by:

A_initial = (1.24 m)^2

For the final circular shape, the magnetic flux through the loop (Φ_final) is given by:

Φ_final = B * A_final

Where:
A_final = π * r^2 (area of the circular loop)

Since the loop is now circular, we need to find the radius (r) using the given length of the loop (1.24 m):

Circumference of the circle = 2πr = 1.24 m
Solving for r:
r = 1.24 m / (2π)

Now, we can calculate the final area (A_final) of the circular loop:

A_final = π * (1.24 m / (2π))^2

Next, we calculate the change in magnetic flux:

ΔΦ = Φ_final - Φ_initial

Finally, we can substitute the values into the formula for the average magnitude of the induced emf:

ε = ΔΦ/Δt

Substitute the values and calculate the average magnitude of the induced emf.