A wire which moves with a speed of 4.6ms–1 is 17.0cm long and has negligible resistance. The magnitude of the magnetic field is 0.25T and the resistance of the u–shaped conductor is 25.00ohms at a given instance. Calculate the induced emf and the current flowing in the u–shaped conductor
To calculate the induced EMF (ε) in the wire, we can use Faraday's law of electromagnetic induction, which states that the EMF induced in a closed loop is equal to the rate of change of magnetic flux through the loop.
The magnetic flux (Φ) through a loop is given by the formula:
Φ = B * A
where B is the magnitude of the magnetic field and A is the area of the loop.
In this case, the loop formed by the wire has a length of 17.0 cm and negligible width, so the area of the loop can be approximated as the product of the length and the width (since the width is negligible):
A = L * w
where L is the length of the loop and w is the width. Since w is negligible, we can ignore it.
Given that the length of the loop (L) is 17.0 cm = 0.17 m, and the magnitude of the magnetic field (B) is 0.25 T, we can calculate the flux (Φ) through the loop:
Φ = B * A = B * L * w = B * L
Φ = 0.25 T * 0.17 m = 0.0425 T·m²
Next, we need to calculate the rate of change of magnetic flux through the loop, which is equal to the induced EMF (ε) divided by the time (Δt):
ε = ΔΦ / Δt
Given that the wire moves with a speed of 4.6 m/s, the time it takes to move from one end of the loop to the other is equal to the length of the loop divided by the speed:
Δt = L / v = 0.17 m / 4.6 m/s = 0.037 s
Substituting the values into the equation, we can calculate the induced EMF:
ε = ΔΦ / Δt = (0.0425 T·m²) / (0.037 s) ≈ 1.149 V
Therefore, the induced EMF in the wire is approximately 1.149 V.
To calculate the current flowing in the U-shaped conductor, we can use Ohm's law:
I = ε / R
Given that the resistance of the U-shaped conductor is 25.00 Ω, we can calculate the current:
I = ε / R = (1.149 V) / (25.00 Ω) ≈ 0.046 A
Therefore, the current flowing in the U-shaped conductor is approximately 0.046 A.