Physics Asked on April 5, 2021
B field at distance from the center of a ring. And the set up I built.
begin{equation}
{B}_z = frac{mu _0}{2}frac{IR^2}{(sqrt{z^2+R^2})^{3/2}}
end{equation}
My voltage through the large ring is 20 volts peak to peak at a frequency of 212kHz. I measure the voltage induced in my small red receiving coil. Should follow faradays Law.
begin{equation}
{mathcal{E} = -N frac{d Phi_B}{d t} }
end{equation}
My B field has a frequency of 212kHz from my voltage. so the derivative of my Bz pops out the constant 424000π which increases ε. There is a capacitor on my receiving coil to eliminate impedance. It is a band pass filter. With the coil inductance and the cap value my system resonates at 212kHz. I know my C and L so:
begin{equation}
f_{0} = frac{1}{2pi sqrt{LC}}
end{equation}
Its the derivative from Faradays law that’s throwing me off. If i choose a different cap value so it eliminated impedances at say a giga hertz. Then the induced voltage would have a coefficient π x 2 x 10^9 from the derivative of my oscillating B field?
That would be huge. My set up right now induces like 4 volts from 5 cm away. If i ran my system at a gig hertz with the correct cap then it would induce like 5000 times more voltage? Pretty sure I’m confused somewhere. Here’s my data
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