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

Answer 1

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.