A rectangular loop with sides l and w are inside of a region with constant magnetic field B is pulled to exit the region with velocity v.
a) find the magnitude of the net induced emf on the loop
b) find the direction of the current induced on the loop
To find the magnitude of the net induced emf on the loop, you can use Faraday's law of electromagnetic induction. According to Faraday's law, the induced emf in a loop is equal to the rate of change of magnetic flux passing through the loop.
The magnetic flux, denoted by Φ, is given by the formula Φ = B * A, where B is the magnetic field strength and A is the area of the loop perpendicular to the magnetic field.
Now, let's calculate the rate of change of magnetic flux. Since the loop is being pulled out of the region with a velocity v, the area of the loop that is perpendicular to the magnetic field is changing over time.
The area A of the loop is given by the formula A = l * w, where l is the length of the loop and w is the width of the loop. Since only the length of the loop is changing, we can express the rate of change of the area as dA/dt = (dl/dt) * w.
Using the chain rule, we have dl/dt = v, since v is the velocity at which the loop is being pulled out of the region.
Now, let's substitute the expressions for A and dl/dt into the formula for the rate of change of magnetic flux:
dΦ/dt = B * dA/dt
= B * (dl/dt) * w
= B * v * w
Finally, we can conclude that the magnitude of the net induced emf on the loop is given by:
emf = | - dΦ/dt |
= | - B * v * w |
= B * v * w
To find the direction of the current induced on the loop, you can use Lenz's law. Lenz's law states that the direction of the induced current is such that it opposes the change in magnetic flux that caused it.
In this case, as the loop is being pulled out of the region with the magnetic field, the change in magnetic flux is a decrease. To oppose this decrease, the induced current flows in a direction that creates a magnetic field that opposes the original magnetic field.
Therefore, to determine the direction of the induced current, use your right hand and curl your fingers in the direction of the original magnetic field B. Your thumb will point in the opposite direction, which gives you the direction of the induced current in the loop.