This isn't a problem, but I wanted to get some clarification of Lenz's law and Faradays law. So if you have a solenoid of wiresand you take a magnet and move it through the solenoid with a velocity v that magnet will induce a current into the wire according to the right hand rule. Thumb points in the direction of v and we curl our fingers around the solenoid. here is a super crappy picture:
But according to faraday and current in a wire will produce a magnetic field that opposes the magnet and pushes it the other way. I understand that, but looking at the equation:
I don't really understand how this tells us that the magnet will experience a force in the opposite direction. I don't fully understand what emf means besides that we can think about it as voltage and why it is equal to the negative of the time rate change of the flux. This is equation is saying that a changing magnetic field will induce an emf in our wire, but what is that emf? Does this mean we have an opposing current or something? Is emf the force that is pushing the magnet is the opposite direction that it is moving? if emf is induced in the wire, what does that mean exactly? voltage across a wire? Change in potential across a wire=0?? I feel like I don't have an intuitive sense of all of this...
The Attempt at a Solution