# Emf in the Archimedean spiral

**Electricity and Magnetism**Level 4

A wire is bent into the shape of an planar Archimedean spiral which in polar coordinates
is described by the equation
\[ r= b \theta. \]
The spiral has \(N=100\) turns and outer radius \(R=10~\mbox{cm}\) (\(R\) 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
\[ B=B_{0}\cos(\omega t)\] where \(B_{0}=1 ~\mu \mbox{T}\) and \(\omega=2\times 10^{6}~\mbox{s}^{-1}\). Determine, the amplitude of the emf **in Volts** induced in the circuit.