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A wire is bent into the shape of an planar Archimedean spiral which in polar coordinates is described by the equation
The spiral has N=100 turns and outer radius
R=10 cm (R is the distance from point O to point T). Note that in the figure below we show a spiral having only 3 turns. The circuit is placed in a homogeneous magnetic field perpendicular to the plane of the spiral. The time dependence of the magnetic field induction is given by
B=B_0 cos (ωt)
B_0=1 μT and ω=2×10^6 s−1
Determine, the amplitude of the emf in Volts induced in the circuit.

  • Physics -

    ℰ = -N•dΦ/dt = -N•d(B₀Scosωt)/dt =
    = NB₀Sωsinωt,
    ℰ max= NB₀Sω,
    Without the figure, I believe that S=πR² =>
    ℰ max= NB₀πR²ω =
    =100•10⁻⁶•3.14•0.1²•2•10⁶ =6.28 V

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