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Multiple Choice
A tightly-wound 200-turn rectangular loop has dimensions of 40cm by 70cm. A constant magnetic field of 3.5T points in the same direction as the normal of the loop. If the dimensions of the loop change to 20cm by 35cm over 0.5s, with the number of turns remaining the same, what is the induced EMF on the rectangular loop?
A
48 V
B
97 V
C
294 V
D
588 V
E
0 V
Verified step by step guidance
1
First, understand that the problem involves electromagnetic induction, specifically Faraday's Law of Induction, which states that the induced electromotive force (EMF) in a closed loop is equal to the negative rate of change of magnetic flux through the loop.
Calculate the initial magnetic flux (Φ_initial) through the loop using the formula: Φ = B * A, where B is the magnetic field strength (3.5 T) and A is the area of the loop. The initial area A_initial is 40 cm * 70 cm. Convert these dimensions to meters before calculating the area.
Calculate the final magnetic flux (Φ_final) after the loop's dimensions change. The final area A_final is 20 cm * 35 cm. Again, convert these dimensions to meters before calculating the area.
Determine the change in magnetic flux (ΔΦ) by subtracting the final magnetic flux from the initial magnetic flux: ΔΦ = Φ_final - Φ_initial.
Use Faraday's Law to find the induced EMF (ε) in the loop: ε = -N * (ΔΦ/Δt), where N is the number of turns (200) and Δt is the time over which the change occurs (0.5 s). Calculate the rate of change of flux and multiply by the number of turns to find the induced EMF.