How Does the Direction of a Magnetic Field Affect Induced EMF in a Loop?

[Vanessa23]

Homework Statement

a) If B (magnetic field) is perpendicular to the plane of a circular loop, then is it true that when B increases the induced emf is clockwise and when the B decreases the emf is counterclockwise? Or do you need to know whether it is pointing into/out of the page? Or would you be able to use the graph of B on the z-axis vs time graph to figure out the direction?

b) I am getting confused with emf versus induced emf. Are they the same thing? For instance, in the following equations is "E" induced emf in all of them for the same problem? And if they are, then in a different problem are they all emf or does the equations not apply to emf?

Homework Equations

E=-NdB/dt
E=Blv
E=NBAwsin(wt)

The Attempt at a Solution

 

[blochwave]

The emf is what is induced by electromagnetic induction in these problems. It IS an induced emf in that sense, but just saying emf should be clear. Emf is basically a voltage but the source isn't from what you'd normally expect a potential difference to arise from. The term is also used in batteries, for example

You could think of it like "the induced voltage" if it helps but know that it's not quite accurate.

a) is explained by Lenz's Law. Your question as worded is awkward, don't think of it as increasing or decreasing per se, think of it as increasing in one direction or the other(it's the CHANGE that matters)

To help remember, note that it's almost like the system has "inertia." The B field is going to change, one way or the other, and induce a current in the loop. The current in the loop is going to cause a magnetic field. The direction of the current is going to be such as to create a magnetic field that OPPOSES the CHANGE in the original magnetic field

When determining the direction you don't give two craps about the original magnitude of the B field or which direction it was pointing, you care which direction it's CHANGING.

So if I have a wire loop sitting on my desk and a B field pointing up that's increasing(ie it was pointing up and is now getting bigger in the up direction)the induced current, just from the right hand rule, is going to be clockwise, so that the B field that comes from the induced current will oppose the change.

If I had that same setup but the original B field was pointing DOWN but decreasing(ie it was originally pointing down but is now growing in the up direction, even if it's not pointing up yet)the induced current would still be flowing the same direction

This is all described by your first equation(the induced emf is opposite the direction of dB/dt)

The second equation has to do with flowing conductive liquids or something, right?

The third one, I'm unsure if it belongs

 

[Vanessa23]

Thank you for the explanation of emf as induced emf. Your explanation makes it much more clear.
So if you are given a graph of B on the z axis with time on the x-axis when you knew the Bfield was perpendicular to the plane of the loop (which is on the paper) you could say that the emf was going clockwise when B is positive or negative with a positive slope; and counterclockwise when B is positive or negative with a negative slope? Because a positive slope would indicate that the B field is increasing in +z direction, so the emf would need to oppose it in the clockwise direction, if it was already negative and becoming more negative then it would need to oppose it in the counterclockwise direction. If it was originally negative but is increasing towards the x-axis (becoming less negative) then the emf would need to be in the clockwise direction. Likewise, if it was positive but becoming less positive then the emf would have to be counterclockwise.

Is that correct?