An induction furnace consists of a coiled copper rod attached to a radio frequen

Question

An induction furnace consists of a coiled copper rod attached to a radio frequency (RF) generator. The furnace generates heat by inducing eddie currents in a work-piece placed the center of the coil. These currents, in turn, heat the piece through ohmic heating. The technique is used in a process called "Float Zone Refining" for materials like silicon to remove defects and impurities from the crystal lattice. A similar technique is used in induction cooktops to heat metal cookware. The power is transmitted by the time-varying magnetic field at the center of the coil. Making the usual simplifying assumptions for a solenoid, calculate the maximum power that would be transmitted to a work piece at the center of an 8 turn coil with a diameter of 210 mm and a length of 315 mm which carries a sinusoidally varying current of I max = 10.0 Amperes at a frequency f = 13.56 M Hz. Assume that the permeability of the work piece is the same as the permeability of free space.

Explanation / Answer

time = 1/freq

B = uonIsin(wt) --> sin(wt) ~= 1 --> unI = uoNAI/L = 2.8*10^-3 T

By faraday's law:

uo = 1/2Luo * B2 = power of a volume dt = E/V * - I dI/dt

Some shifting around:

(VB2/2LIEuo ) dt = dI

Integrate both sides from 0 to t with respect with t. and 0 to I on the other:

VB2t/2LEuo = P = 4000 W

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