Answer
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Step 1:I'll solve this problem step by step, carefully following the LaTeX formatting guidelines:
Step 2:: Calculate the Area of the Coil
- Number of loops: $$N = 20
- Area of the coil: A = a \times b = (0.0800 \mathrm{~m}) \times (0.120 \mathrm{~m}) = 9.60 \times 10^{- 3} \mathrm{~m}^{2}
Step 3:: Determine the Rate of Change of Magnetic Flux
- Magnetic field: $$B = 3.00 \mathrm{~T}$$ (pointing into the page)
- Velocity: v = 5.00 \times 10^{- 2} \mathrm{~m/s}
Step 4:: Calculate Induced EMF for Different Situations
- Induced Current: $$I = \frac{|\epsilon|}{R} = \frac{1.20}{8.00} = 0.150 \mathrm{~A}$$ (clockwise)
The induced EMF will depend on the fraction of the coil in the magnetic field. Situation 1: Coil Completely Outside the Field Situation 2: Half the Coil in the Field Situation 3: Coil Entirely in the Field Situation 4: 75% of Coil Exited the Field
Step 5:: Explanation of Part (b)
The induced EMF depends on the rate of change of magnetic flux. When the coil is moving at a constant velocity, the rate of change of flux is the same whether 25% or 50% of the coil is in the field, resulting in the same induced EMF.
Final Answer
(a) See the detailed calculations in Step 3 (b) The induced EMF is the same because the rate of change of magnetic flux is constant during the linear motion of the coil.
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