A rectangular loop of wire with sides 0.196 and 0.584 m lies in a plane perpendicular to a constant magnetic field (see part a of the drawing). The magnetic field has a magnitude of 0.723 T and is directed parallel to the normal of the loop's surface. In a time of 0.249 s, one-half of the loop is then folded back onto the other half, as indicated in part b of the drawing. Determine the magnitude of the average emf induced in the loop.

Oh, it's time for some physics fun!

Well, when it comes to electromotive force (emf), things can get a little electrically exciting. So, let's dive right in!

In this case, we have a rectangular loop of wire folding back onto itself in a magnetic field. To determine the magnitude of the average emf induced in the loop, we can use Faraday's Law of electromagnetic induction.

Faraday's Law states that the emf induced in a circuit is equal to the rate of change of magnetic flux through the loop. The magnetic flux through a loop is given by the product of the magnetic field strength and the area of the loop.

So, let's break it down!

The loop has sides of length 0.196 m and 0.584 m. When it folds back, we effectively have two parallel loops. The area of one loop is given by A = 0.196 m * 0.584 m.

Now, we need to find the rate of change of magnetic flux through the loop. The magnetic field has a magnitude of 0.723 T and is parallel to the normal of the loop's surface.

Since the magnetic field is constant and parallel to the normal, the change in flux is zero. Therefore, there is no change in flux, and the average emf induced in the loop is also zero.

So, the average emf induced in the loop is zero. Sorry if that's a bit shocking, but remember, not all physics problems have electrifying solutions!

To determine the magnitude of the average emf induced in the loop, we can use Faraday's Law of electromagnetic induction, which states:

EMF (ε) = -N(dΦ/dt)

Where:
- ε is the induced emf
- N is the number of turns in the loop
- dΦ/dt is the rate of change of magnetic flux

In this case, the magnetic field is constant and parallel to the normal of the loop's surface. Thus, the magnetic flux (Φ) through the loop can be calculated as the product of the magnetic field (B) and the area (A) of the loop:

Φ = B * A

Since the loop is rectangular with sides 0.196 m and 0.584 m, the area is given by:

A = length * width = (0.196 m) * (0.584 m) = 0.114464 m²

Now, let's calculate the magnitude of the average emf induced in the loop.

Step 1: Calculate the magnetic flux (Φ)
Φ = B * A = (0.723 T) * (0.114464 m²) = 0.082977792 T.m²

Step 2: Calculate the rate of change of magnetic flux (dΦ/dt)
The time taken for one-half of the loop to be folded back onto the other half is given as 0.249 s. During this time, the length and width of the loop remain the same. Therefore, the change in the area (ΔA) of the loop is zero. As a result, the rate of change of magnetic flux is also zero.

dΦ/dt = 0

Step 3: Calculate the magnitude of the average emf (ε)
ε = -N(dΦ/dt) = -N * 0 = 0

Therefore, the magnitude of the average emf induced in the loop is 0.

To determine the magnitude of the average emf induced in the loop, we need to use Faraday's law of electromagnetic induction.

Faraday's law states that the induced electromotive force (emf) in a circuit is equal to the rate of change of magnetic flux through the circuit.

The formula to calculate the emf is given by:

emf = (change in magnetic flux) / (change in time)

1. Calculate the change in magnetic flux:
The magnetic flux through a loop is given by the formula:

magnetic flux = magnetic field strength * area * cosine(theta)

where
- magnetic field strength: 0.723 T (given)
- area: area of the loop (0.196 * 0.584 m^2)
- theta: angle between the magnetic field and the normal to the loop's surface (which is 0 degrees since they are parallel)

So, the initial flux is: initial_flux = 0.723 * (0.196 * 0.584) * cos(0°)

2. Determine the change in time:
The problem states that in a time of 0.249 s, one-half of the loop is folded back onto the other half. Since the magnetic field remains constant during this time, we don't need to consider the time for this calculation.

3. Calculate the change in magnetic flux:
When the loop is folded back onto itself, the area through which the magnetic flux passes is now half of the original area.

So, the final flux is: final_flux = 0.723 * (0.196 * 0.584 / 2) * cos(0°)

4. Calculate the change in magnetic flux:
(change in magnetic flux) = (final flux) - (initial flux)

5. Calculate the average emf:
Emf = (change in magnetic flux) / (change in time)

Plug in the values and calculate to find the answer.