Question

The near-simultaneous, yet independent works of Faraday and Henry have shown, in 1831 and 1832, respectively, that a change in magnetic flux through a spiral coil results in an induced electromotive force. Examine the qualitative and quantitative aspects of induction, as predicted by those two physicists.

A magnetic field produced by a solenoid is proportional to current; therefore, we can infer that for two stationary coaxial solenoids, the flux through the secondary is proportional to the current passing through the primary coil. If the theories of Faraday and Henry are correct, a sinusoidal current of form I(t) = I₀ should produce a sinusoidal induced voltage:

V(t) dI/dt *cos t so that V(t) = V₀*cos t with V₀

A sensible way to investigate Faraday’s law qualitatively is to establish that the voltage signal has the same period as the current, and, noting that x=sin(PI/2 + x), the time shift between current and voltage should correspond to a-(PI/2) phase difference (a quarter of a full period ahead, or “phase quadrature”). The two laws of proportionality for V₀ should complete the argument.

Here is the given data.

Frequency, f [Hz] | Current Ampl.,A [A] 10 20 30 40 50 0.01785 0.01787 0.01785 0.01787 0.01786 ▼ | Current Freq, . B [rad/s): | Current Phase, C [rad] 62.07 130.79 187.69 250.13 313.81 0.33813 3.929 5.1019 3.4467 2.3267 | Emf Ampl. A [V] ▼ | Emf Freq., B [rad/s1-Emf Phas, C [rad1 1.6703 5.03 6.077 4.2758 2.979 6.9908 13.53 17.825 21.21 22.86 62.064 130.79 187.68 250.13 313.76

1.) Describe the emf signal.

(would it just be a sin wave?)

2.) Use the fact that T=2PI/ to calculate the periods, and that time shifts can be obtained from the fit constants usingT= | (C₁/B₁)-(C₂/B₂) |

3.) Calculate the amplitudes from the given data in the second table.

Answer 1

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