A long, narrow rectangular loop of wire is moving toward the bottom of the page with a speed of 0.021 m/s (see the drawing). The loop is leaving a region in which a 2.7 T magnetic field exists; the magnetic field outside this region is zero. During a time of 3.0 s, what is the magnitude of the change in the magnetic flux?
flux=area*dB/dt
To solve this problem, we need to use Faraday's law of electromagnetic induction, which states that the emf induced in a circuit is equal to the rate of change of magnetic flux through the circuit.
The magnetic flux (Φ) through a loop is given by the equation: Φ = B * A, where B is the magnetic field and A is the area of the loop.
In this case, the magnetic field is 2.7 T, and the loop is moving through this field, so the area of the loop changes over time. The change in magnetic flux (ΔΦ) can be calculated by subtracting the initial magnetic flux from the final magnetic flux:
ΔΦ = B * (A_final - A_initial)
Given:
Velocity of the loop (v) = 0.021 m/s
Time taken (Δt) = 3.0 s
To find the change in area (ΔA), we can use the formula: ΔA = v * Δt
ΔA = 0.021 m/s * 3.0 s
Now, we can substitute the values into the equation for the change in magnetic flux:
ΔΦ = (2.7 T) * ΔA
ΔΦ = (2.7 T) * (0.021 m/s * 3.0 s)
Simplifying the equation:
ΔΦ = 2.7 T * 0.063 m
Calculating the magnitude of the change in magnetic flux:
|ΔΦ| = 0.1701 T·m²
Therefore, the magnitude of the change in the magnetic flux is 0.1701 T·m².