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Multiple Choice
A square conducting wire of side length 4 cm is in a 2 T magnetic field. It rotates such that the angle of the magnetic field to the normal of the square increases from 30° to 60° in 2 s. What is the induced current on the wire if its resistance is 5 mΩ?
A
0.85 A
B
0.12 A
C
1.2 A
D
1.39 mA
Verified step by step guidance
1
First, calculate the initial magnetic flux (Φ_initial) through the square loop. The formula for magnetic flux is Φ = B * A * cos(θ), where B is the magnetic field strength, A is the area of the loop, and θ is the angle between the magnetic field and the normal to the loop. Use θ = 30° for the initial angle.
Next, calculate the final magnetic flux (Φ_final) using the same formula, but with θ = 60° for the final angle.
Determine the change in magnetic flux (ΔΦ) by subtracting the initial magnetic flux from the final magnetic flux: ΔΦ = Φ_final - Φ_initial.
Calculate the induced electromotive force (emf) using Faraday's law of electromagnetic induction, which states that the induced emf is equal to the negative rate of change of magnetic flux through the loop: emf = -ΔΦ / Δt, where Δt is the time interval over which the change occurs (2 seconds in this case).
Finally, use Ohm's law to find the induced current (I) in the wire. Ohm's law states that I = emf / R, where R is the resistance of the wire (5 mΩ).