Could someone please explain to me why we want to take the "magnitude" of the emf?
[Physics] Positive emf? What does positive emf mean
electromagnetismmaxwell-equations
Related Solutions
If you move a wire through a magnetic field so that the wire, the motion, and the magnetic field are all mutually orthogonal, them there is a magnetic force on the charges (because of the motion) that has a component in the direction of the wire (because we arranged the directions the right way). The energy comes from the agent moving the wire, but there is a real force.
When electric and magnetic forces were considered separate, it was merely an experimentally observed fact that if you changed the magnetic field in time there would be a force driving the charges through a wire. But if you look at that magnetic force above, but consider the situation in the frame of the moving wire, there is no magnetic force in that frame, but there is still a force.
You can consider that to be the real reason that changing magnetic fields induce electric fields.
Inconsistency between two theories just means that there are statements that one theory says are true, and the other says are false.
An easier example than the one you're asking about is the inconsistency between Newtonian mechanics and special relativity. Newtonian mechanics says that if you keep applying a force to a material object, it will eventually go faster than the speed of light, c. Special relativity says that this statement is false.
Your example of Newtonian mechanics versus Maxwell's equations is a lot more subtle. If you'd asked someone in 1890, they probably would have said that Maxwell's equations were consistent with Newtonian mechanics, but they simply described different aspects of nature. In order to maintain this consistency, they were forced to say that Maxwell's equations had their simplest form in one preferred frame of reference, which was believed to be the frame of the ether. What they didn't realize was that the transformation of distance and time measurements from one frame of reference to another was not described correctly by the equations they'd been assuming. Using the correct, relativistic transformations, Maxwell's equations have the same form in all frames. Today, physicists think of Maxwell's equations as being inherently based on special relativity; but that wasn't how people in 1890 thought of them.
Best Answer
To solve induction problems, you first need to define an orientation of the coil, this orientation induces a positive a negative side for any surfaces whose boundary is the coil, then you can compute the magnetic flux and at last the emf. A positive result means the emf runs a current in the positive orientation of the coil. Since you don't know much about the geometry of B, you can't decide if the emf is positive or negative, that is why you are not asked for the sign.