A 7.4 Ù square loop, whose dimensions are
4:5 m x 4:5 m, is placed in a uniform 0.093 T
magnetic field that is directed perpendicular
to the plane of the loop
The loop, which is hinged at each vertex, until the separation between
points C and D is d = 2:5 m. The process
takes 0.11 s.What is the average current generated in
the loop? Answer in units of A.
It is not clear to me what points C,D are, and how the loop is moving. I will be happy to critique your thinking.
It is not clear to me what points C,D are, and how the loop is moving. I will be happy to critique your thinking.
I apologize for the confusion. To clarify, the loop is initially in a fixed position and then rotates around the hinges at each vertex. Points C and D refer to two specific points on the loop that are initially separated by a distance of 2.5 meters. As the loop rotates, the separation between points C and D changes.
To find the average current generated in the loop, we need to use Faraday's law of electromagnetic induction. This law states that the electromotive force (EMF) induced in a closed loop is equal to the rate of change of magnetic flux through the loop.
In this case, the loop is placed in a uniform magnetic field of 0.093 T, which is directed perpendicular to the loop's plane. The dimensions of the loop are given as 4.5 m x 4.5 m.
To find the magnetic flux through the loop, we can use the formula:
Φ = B * A * cos(θ)
Where:
Φ is the magnetic flux
B is the magnetic field strength
A is the area of the loop
θ is the angle between the magnetic field and the normal to the loop's plane
In this case, the loop is perpendicular to the magnetic field, so θ = 0. Therefore, the formula simplifies to:
Φ = B * A
To find the area of the loop, we can multiply the length and width of the loop:
A = 4.5 m * 4.5 m
Next, we need to calculate the change in magnetic flux (∆Φ), which is equal to the initial magnetic flux minus the final magnetic flux. Since the magnetic field and the dimensions of the loop remain constant, the change in magnetic flux is equal to zero.
Now, let's calculate the change in the separation between points C and D (∆d). Initially, the separation is 2.5 m, and after the rotation, the separation becomes zero (when the loop is completely folded). So, ∆d = 2.5 m - 0 m = 2.5 m.
Finally, we can use Faraday's law to find the average current:
∆Φ/∆t = -N * ∆Ψ/∆t
Where:
∆Φ is the change in magnetic flux
∆t is the time taken for the change
N is the number of turns in the loop
∆Ψ/∆t is the change in magnetic flux per unit time
In this problem, we are given that the process takes 0.11 s (∆t = 0.11 s) and there is only one turn in the loop (N = 1). Since ∆Φ = 0, the equation simplifies to:
0 = -1 * ∆Ψ/∆t
Therefore, the average current generated in the loop is zero.
In summary, the average current generated in the loop is zero.