A loop is rotated to the new orientation in 1s. What is the magnitude of the average induced EMF?
B= 2T
60 degrees
n again is sticking out of the page
To find the magnitude of the average induced EMF, we need to use Faraday's law of electromagnetic induction. According to Faraday's law, the induced EMF is equal to the rate of change of magnetic flux through the loop.
To calculate the magnetic flux, we need to consider the change in the magnetic field and the area of the loop. In this case, the magnetic field is given as B = 2 Tesla, and the area of the loop is not specified.
Since the loop is rotated to a new orientation, the change in magnetic flux can be calculated as the product of the change in angle and the magnetic field.
Given that the loop is rotated by 60 degrees, the change in angle is 60 degrees - 0 degrees (initial orientation) = 60 degrees.
Now we need to find the area of the loop. You mentioned that "n" is sticking out of the page. Assuming "n" represents the normal vector perpendicular to the loop, the area of the loop can be chosen as the magnitude of this normal vector.
The magnitude of a normal vector is always 1. Hence, the area of the loop is 1 square unit.
Substituting the values into the equation for the change in magnetic flux:
Change in magnetic flux = B * change in angle * area
= 2 Tesla * 60 degrees * 1 square unit
Now, simplify the equation:
Change in magnetic flux = 2 * 60 * 1 Tesla-degree-square unit
Since 1 degree = π/180 radians, the units cancel out:
Change in magnetic flux = 2 * 60 * (π/180) Tesla-radian-square unit
= 2 * (π/3) Tesla-radian-square unit
This gives us the change in magnetic flux. However, we need the rate of change of magnetic flux to find the induced EMF. Since the loop takes 1 second to rotate, the rate of change of magnetic flux is simply the change in magnetic flux divided by the time:
Rate of change of magnetic flux = Change in magnetic flux / Time
= (2 * (π/3) Tesla-radian-square unit) / 1 second
Finally, we have the rate of change of magnetic flux, which is equal to the induced EMF. Hence, the magnitude of the average induced EMF is:
Magnitude of induced EMF = 2 * (π/3) Tesla-radian-square unit / 1 second
Please note that the final answer will depend on the units used for magnetic flux, time, and the resulting induced EMF.