This is the second year I’ve taught AP Physics C: E&M, and we’re getting to the final leg of the course: electromagnetism. I was preparing the unit’s opening activities when I came up against the struggles of Lenz’s Law. One pesky negative sign within Faraday’s Law creates more trouble than just about anything in this class.
At this point in the year, my students have studied electrostatics, including potential and Gauss’ Law, RC circuits, and magnetostatics, including Ampere’s Law.
I’ve never really understood how to use Lenz’s Law to consistently predict the correct direction of an induced current. I was trying to figure it out again a few days ago, and it ended with some choice 4-letter words and my head on my desk.
But I’ve got it now! And I’ve come up with an activity that will help students understand it as well all thanks to the HTML5 version of PhET’s Faraday’s Law simulation.
The HTML5 version is particularly good because of the option to display the magnetic field lines coming from the magnet. This is the key to the entire activity as it’s what allows students to reason through how the magnetic flux through the wire loop is changing. It also being an HTML5 sim allows it to run on phones and tablets. Also, it’s FREE.
Faraday’s Law First
I had students first explore Faraday’s Law through the old java version of the sim. This one allows you to vary the size of the loops, which the HTML5 version doesn’t. I ask students simply to play with the sim and figure out the conditions required for current to be generated in the wire as well as to list the factors that affect the magnitude and direction of the current. Students don’t have much trouble figuring all of this out.
We then have a quick discussion on how to predict the direction of the induced current, and this is where things get sticky. There are lots of patchwork theories that arise that are basically a list of if-then statements involving the direction of motion of the north or south end of the magnet relative to the loop.
This is ultimately unsatisfying because a list of if-then’s is not a good scientific model, especially situations that aren’t “moving a bar magnet near a wire loop.” I then take a few minutes to review flux, which they’d seen from electrostatics, and then introduce magnetic flux as basically the same thing, but with magnetic fields.
I conclude the discussion by emphasizing that looking at this from a “how is the flux changing” perspective is more generalized than “which end of the magnet is moving how” perspective and, thus, will result in a much more generalized and useful model.
The goal of the activity is to collect “data” by drawing before-and-after pictures of the magnet moving into and out of the loop. Students use each set before-and-after drawings to figure out the change in magnetic flux due to the motion of the magnet, the voltage reading (whether it’s positive or negative) to determine the direction of the current, and then the right-hand rule (which they know from the previous unit) to figure out the field created by the wire.
Here’s one example of moving the north end of the magnet towards the loop. Having the “field lines” box checked is essential.
In the “before” snapshot, students draw an arrow* indicating the direction of the flux through the loop. In the “after” snapshot, students draw another arrow showing the direction of the flux, longer if the flux increased and shorter if it decreased, then a dashed arrow showing the change in the flux. They also use the voltage (negative voltage = flow from positive terminal to negative terminal, positive = opposite) to determine the direction of the current, which they draw, and then they draw the direction of the field in the wire due to that current.
To figure out if the flux increases or decreases, they use the density of the field lines in the loop. More density = greater field = greater flux. The direction of the change is figured out by looking at the direction that they had to stretch or compress their initial flux arrow to turn it into the final flux arrow. For example, the first picture has a flux arrow pointing to the left, and the after has one longer, but still pointing to the left. If you wanted to make the first one look like the second, you’d have to stretch it to the left. Therefore, the change is to the left.
Students look at 4 scenarios, which require 2 drawings each:
- The north side of the magnet moves from to the right of the loop to the front edge being inside the loop (pictured above).
- The far end of the south side of the magnet moves from the center of the loop to the left of the loop (pictured below).
- The far end of the south side of the magnet moves from the left of the loop to the center of the loop.
- The far end of the north side of the magnet moves from the center of the loop to the right of the loop.
Basically they pull the magnet into and out of the loop from the right, then reverse and pull it into and out of the loop from the right.
*Since flux isn’t a vector, I’ve been careful not to call them vectors. Though, what we’re kind of doing is vector subtraction to figure out the direction of the change. I’m not quite sure why we can treat it like a vector and it still work out that way. Oh well.
Once they’re done, they’ve got 8 drawings with all kinds of arrows, so it’s kind of a mess. The goal is to see a pattern that they can use to predict the direction of the induced current based on the change in flux. When they’re eventually figuring this out on their own, I want them to think about it like this:
- Figure out the direction of the change in flux.
- Figure out the direction of the field that would oppose that change.
- Use the right-hand-rule to figure out the current required to generate that field.
To facilitate that, I had my students make a summary page that filtered out most of the data so that they could easily see the pattern. I put this up on the board and told them to fill in the rest from their data once they finished.
The conclusion to this was to figure out the pattern between the direction of the change in flux and the direction of the induced magnetic field. If done correctly, all of them should be opposite of one another, which students easily saw.
Here is an example of some student work.
A few other things
The devil is in the details for this activity, so I walked through the first set of drawings with everyone to make sure they were doing everything correctly. I told them that they needed to draw the same number of field lines for each snapshot (I chose 6, the simulation draws 8), and that when drawing them, they needed to make sure and basically draw them as they’re drawn on the simulation. Doing this right is key to being able to use the density of field lines to deduce the magnitude of the field/flux within the loop.
My students also have lots of practice in figuring out the direction of change by looking at before and after vectors. Even if they hadn’t, explaining it as I did above (by looking at the direction required to stretch or compress one vector to the other), I don’t think it would have been too difficult for them to figure out.
I also made sure to check on each group frequently to make sure they were doing everything correctly because, again, getting everything correct is key to seeing the pattern at the end.
If you have any suggestions for improving this, please let me know! If you use this (or something similar) and would like to share your experience with it, please do so as well! And if you need help or clarification with anything here, leave a comment, and I’ll do my best to help out.