Posted by **Steven** on Monday, July 29, 2013 at 5:38am.

A wire is bent into the shape of an planar Archimedean spiral which in polar coordinates is described by the equation

r=bθ.

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)

where

B_0=1 μT and ω=2×10^6 s−1

Determine, the amplitude of the emf in Volts induced in the circuit.

- Physics -
**Elena**, Monday, July 29, 2013 at 6:07am
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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