I am not sure what simplifying assumptions could be made to calculate the force of eddy currents, but the magnetic field produced by the eddy currents should be small compared to the magnetic field produced by current through the coil. But good luck!
I am not sure what you are looking for when you say magnitude of eddy currents. Eddy currents are currents induced by a magnetic field, and flow in loops, usually in sheet conductors rather than wires.
The current in the solenoid can be considered analogous to the flow of water in a pipe: the...
Faraday's law is represented in derivative form as
$$\nabla \times \vec{E} = -\frac{d\vec{B}}{dt}$$
In integral form, this is
$$\int_{closedloop} \vec{E} \bullet dl = -\frac{d\Phi_{B}}{dt}$$
Where ##\Phi_{B}## is the magnetic flux or integral of the magnetic flux density over the cross section...
That diagram does not seem helpful.
You have already given the solution for the problem.
Velocity in the horizontal direction is constant.
Acceleration in the vertical direction is constant.
Time can be found by solving for time from the equation for vertical displacement, which you have given...
I would like to point out that the above formulas contain slight errors and will make the corrections shown below.
The Continuous Fourier series coefficients are given by
##a_{n} = \frac{1}{T} \int_0^T X(t)e^{j \frac{-2 \pi nt}{T}}dt## for ##-N<= n<=N##
And to reconstruct the continuous...
Looking at the plot on the right, I cannot tell what N is but it appears that -N<=n<=N but only -5<=n<=5 is shown.
You can find the nth coefficient using the discrete Fourier transform using the equation below and then taking the absolute value. ##a_{n} = \sum_{k = -N}^{N} X(k) e^{-\frac{ 2j\pi...
I got lost as to what you were doing around line 26 but if what you're doing is obtaining Fourier series coefficients and then reconstructing a wave then the following should help.
Continuous function Fourier series coefficients is given by
##a_{n} = \frac{1}{T} \int_0^T X(t)e^{j \frac{-2 \pi...
You are calculating Heat In - Heat Used to melt ots which is not efficiency
From my understading efficieny is ##\frac{what\ you\ want}{what\ you\ put\ in} ##
In this case that would be ##\frac{heat\ to\ increase\ temperature\ +heat\ used\ to\ melt\ ingots}{heat\ in\ from\ melting\...
I am confused by your barometric formula because you seem to be using P for both density and pressure.
In a static air situation and treating air as compressible, we can use the ideal gas law to get
1) ##\rho=\frac{PM}{RT}##
where P is pressure
M is molar mass =28.97
R is the ideal gas...
When doing Norton/Thevenin Equivalent circuits you need## i_{sc}## (short circuit current) and ##v_{oc} ##(open circuit voltage). You correctly found ## i_{sc}## for the short/closed circuit as or 3.84 A.
.
If you solve the open circuit condition you will get ##V_{out}## =4.5 V. Then to get...
Your answer seems right.
In order to incorporate direction into your formula
we have
τ = p×E
so if E is 45 degrees counterclockwise of p then τ is counterclockwise
if E is 45 degrees clockwise of p then τ is clockwise
Your problem doesn't state whether it is 45° clockwise or counterclockwise...