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Zorluk: ZorElectromagnetic Induction

A rectangular coil of 100100 turns with dimensions 0.10 m0.10\text{ m} by 0.20 m0.20\text{ m} is positioned perpendicular to a uniform magnetic field of 0.50 T0.50\text{ T}. The coil is rotated through 90∘90^\circ about an axis perpendicular to the field lines in a time interval of 0.040 s0.040\text{ s}, bringing its plane parallel to the magnetic field. What is the magnitude of the average electromotive force (e.m.f.) induced in the coil in volts?

Cevap: 25 V

Cevap

The magnitude of the average induced electromotive force in the coil is 25 V25\text{ V}.
According to Faraday's law, the induced electromotive force magnitude is E=NΔΦΔtE = N \frac{\Delta \Phi}{\Delta t}. The initial flux through each turn is Φ1=BA=0.50 T×0.020 m2=0.010 Wb\Phi_1 = B A = 0.50\text{ T} \times 0.020\text{ m}^2 = 0.010\text{ Wb}. When rotated parallel to the field, the final flux Φ2\Phi_2 is 0 Wb0\text{ Wb}, so ΔΦ=0.010 Wb\Delta \Phi = 0.010\text{ Wb}. Substituting N=100N = 100 and Δt=0.040 s\Delta t = 0.040\text{ s} yields an induced e.m.f. of 100×0.0100.040=25 V100 \times \frac{0.010}{0.040} = 25\text{ V}.

Adım Adım Çözüm

1
Calculate the cross-sectional area of the rectangular coil.
A=0.10 m×0.20 m=0.020 m2A = 0.10\text{ m} \times 0.20\text{ m} = 0.020\text{ m}^2
The surface area is required to find the magnetic flux passing through each turn.
2
Determine the change in magnetic flux through one turn of the coil.
Initial flux Φ1=BA=0.50×0.020=0.010 Wb\Phi_1 = B A = 0.50 \times 0.020 = 0.010\text{ Wb}; Final flux Φ2=0 Wb\Phi_2 = 0\text{ Wb}; Change ΔΦ=0.010 Wb\Delta \Phi = 0.010\text{ Wb}
When perpendicular to the magnetic field, maximum flux links the coil. Rotating it parallel reduces the flux linking the coil to zero.
3
Apply Faraday's law of electromagnetic induction to calculate induced e.m.f.
E=NΔΦΔt=100×0.010 Wb0.040 s=25 VE = N \frac{\Delta \Phi}{\Delta t} = 100 \times \frac{0.010\text{ Wb}}{0.040\text{ s}} = 25\text{ V}
Faraday's law states that the induced e.m.f. magnitude equals the rate of change of total magnetic flux linkage.

Anahtar Kavram

Faraday's Law of Electromagnetic Induction
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Konular

Electromagnetic Induction

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