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uby
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Please note, I'm not in school anymore -- just a basic physics question!
A conductor is placed inside the coil of an induction heater.
Imagine that the inductor coil has radius R, number of turns N, operating frequency f [Hz], drawing current I = I0 * sin(2*pi*f*t).
The conductor is a cylinder of radius r located concentric to the inductor.
Calculate the magnitude of the induced voltage V at a fixed position on the outer surface of the conductor as a function of time.
V = dO/dt = d(B*A)/dt (where O is the magnetic flux given by B dot A, assuming entire flux goes through cross-sectional area)
B = mu * I / 2*R (where mu is permeability of air = (4*pi)E-7 T*A/m)
V = d(B*A)/dt = d(mu*I*A/2*R)/dt = d(mu*I0*sin(2*pi*f*t)*A/2*R)/dt
V = mu*I0*A/2*R * d(sin(2*pi*f*t))/dt
V = pi*f*mu*I0*A/R *cos(2*pi*f*t)
A = pi*(R^2-r^2) is the area where magnetic field flux operates on conductor
so, for any position on the outer cylinder radius, the maximum magnitude of the induced voltage is found to be:
max(V) = pi^2*(R^2-r^2)*f*mu*I0/R
putting some rough numbers on this:
let R = 0.05 m, r = 0.025 m, f = 100000 Hz, I0 = 20 Amps,
then max(V) = 0.93 VDoes this look correct?
About 1V may not seem like much, but it is for my intended application! And if I need to use megahertz range frequencies the induced voltage goes up by orders of magnitude!
Thanks!
Homework Statement
A conductor is placed inside the coil of an induction heater.
Imagine that the inductor coil has radius R, number of turns N, operating frequency f [Hz], drawing current I = I0 * sin(2*pi*f*t).
The conductor is a cylinder of radius r located concentric to the inductor.
Calculate the magnitude of the induced voltage V at a fixed position on the outer surface of the conductor as a function of time.
Homework Equations
V = dO/dt = d(B*A)/dt (where O is the magnetic flux given by B dot A, assuming entire flux goes through cross-sectional area)
B = mu * I / 2*R (where mu is permeability of air = (4*pi)E-7 T*A/m)
The Attempt at a Solution
V = d(B*A)/dt = d(mu*I*A/2*R)/dt = d(mu*I0*sin(2*pi*f*t)*A/2*R)/dt
V = mu*I0*A/2*R * d(sin(2*pi*f*t))/dt
V = pi*f*mu*I0*A/R *cos(2*pi*f*t)
A = pi*(R^2-r^2) is the area where magnetic field flux operates on conductor
so, for any position on the outer cylinder radius, the maximum magnitude of the induced voltage is found to be:
max(V) = pi^2*(R^2-r^2)*f*mu*I0/R
putting some rough numbers on this:
let R = 0.05 m, r = 0.025 m, f = 100000 Hz, I0 = 20 Amps,
then max(V) = 0.93 VDoes this look correct?
About 1V may not seem like much, but it is for my intended application! And if I need to use megahertz range frequencies the induced voltage goes up by orders of magnitude!
Thanks!