A square loop 23.5 on a side has a resistance of 2.80 . It is initially in a 0.575 magnetic field, with its plane perpendicular to , but is removed from the field in 35.0 .
To determine the induced current in the loop, we can use Faraday's law of electromagnetic induction, which states that the induced electromotive force (EMF) is equal to the rate of change of magnetic flux through the loop.
The magnetic flux (Φ) through the loop can be calculated using the formula:
Φ = B * A * cosθ
Where:
- B is the magnetic field strength (given as 0.575 Tesla)
- A is the area of the loop (since it is a square, A = side length^2)
- θ is the angle between the magnetic field and the direction perpendicular to the loop's plane (which is 90 degrees in this case, as it is perpendicular)
Let's plug in the values to calculate the magnetic flux (Φ):
A = (23.5)^2 = 552.25 square units
θ = 90 degrees
Φ = 0.575 Tesla * 552.25 square units * cos(90 degrees)
Φ = 0.575 Tesla * 552.25 square units * 0
Φ = 0
Since the magnetic flux (Φ) is zero, the induced EMF is also zero.
To calculate the induced current (I), we can use Ohm's Law, which states that the current flowing through a conductor is equal to the voltage divided by the resistance.
I = V / R
In this case, the voltage (V) is equal to the induced EMF, which is zero. Therefore, the induced current (I) in the loop is also zero.
So, when the square loop is removed from the magnetic field in 35.0 seconds, there is no induced current flowing through the loop.