- #1
Matterwave said:Have you tried doing this? Do you know Faraday's law?
Mindscrape said:Hey, from our standpoint it is that easy! You're right, the movement of the coil changes the flux going through it. So figure out how quickly the flux changes, and you've got your answer. You'll have to show us specifically where your work stops if you want more help than that.
Mindscrape said:You can figure out how quick the flux changes by how fast the area is changing. Do you follow? Don't assume the radius, you're given the radius.
Mindscrape said:No, that's not right. Here, let me get you started. It gives you the position function
y=asin(wt)
so you know that the radius of the loop is a. You know that at time t=0 that y=a*0=0. That then shows the loop, with the radius of a, perpendicular to the magnetic field. So,
[tex]\int\int B \cdot da = BA[/tex]
at that point in time. Now hopefully you can see the picture of how your loop is just varying how much flux goes through the loop based on your sine function. It's rotating about the z-axis. Once you've got the flux, it's cake to get the voltage.
Mindscrape said:Ahh, okay, that makes a little more sense with the picture drawn then. Still kind of the same. If v=asinwt, then you have to integrate v w.r.t. time to get position. You still have to relate the flux to the rotation of the loop, and keep in mind that
[tex]\int\int B \cdot da = BAcos(\theta)[/tex]
Mindscrape said:Are you sure about that? If all it does is move up and down in a magnetic field that takes up the entire yz-plane then there is no change in flux and no EMF. Why would the problem give you a sinusoidal position that is translational instead of rotational? That is either wrong or it's a really stupid problem.
Mindscrape said:Well, he could mean a couple of things. He could be talking about a material that develops eddy currents, which are super difficult to calculate. Or if the magnetic field itself has a density associated with it, then you'll get a change in flux from the loop traveling through those different magnitudes of magnetic field. However, you did not list a density of magnetic field in your problem description.
The emf can be calculated using the equation: emf = -N(dΦ/dt), where N is the number of turns in the coil and dΦ/dt is the rate of change of magnetic flux through the coil.
Calculating emf using electrodynamics allows us to understand the relationship between magnetic fields and induced currents, and how they are affected by factors such as coil size and magnetic flux.
Yes, emf can be calculated for non-constant magnetic fields by using the equation: emf = -N(dΦ/dt), where dΦ/dt is the instantaneous rate of change of magnetic flux.
The direction of the induced current is always such that it opposes the change in magnetic flux that caused it. This is known as Lenz's Law. Therefore, the direction of the induced current is always opposite to the direction of the emf.
Yes, calculating emf using electrodynamics is crucial in understanding and designing devices such as generators, transformers, and motors. It is also used in various industries, including power generation, telecommunications, and transportation.