Physics Teachers Forum

Can you please produce a graph of EMF vs distance (starting well outside the coil) as a bar magnet moves into a long solenoid till the entire magnet is in the middle of the solenoid?

There is no single answer to this question because the EMF depends on:
Speed of the magnet, the shape and size and orientation of the magnet (and the magnetic field around it), the shape and size of the solenoid.

To remove the speed dependence, you would need to plot EMF divided by magnet speed. You would need to choose particular sizes and geometries for the magnet and solenoid. You could choose a simple geometry for the solenoid, however, the nature of the magnetic field around a permanent magnet is not trivial. Calculating this is not a back-of-the envelope job.

One could do this experimentally. Rather than moving the magnet at a uniform speed though, I'd oscillate the magnet back and forth around several fixed equilibrium positions and measure the induced EMF (AC). You'd have to be able to calculate the maximum oscillation speed Vmax of the magnet:

Vmax = 2*pi*amplitude*frequency

The amplitude of oscillation would need to be large enough to get a signal (maybe a few mm up to a couple of cm?).

I'd plot the AC EMF/Vmax versus the equilibrium position.

You'd find (qualitatively) that far away, the EMF/Vmax is very low. As you approach, the EMF/Vmax will come to a maximum around the position where the field is relatively strong, but the field lines are not yet very parallel. Once the magnet is inside the solenoid the EMF will be close to zero.

John,
Stephen is correct. There is not one answer. It is very much dependent on all the parameters that Stephen talked about.

Did you have a particular type of magnet (long or short bar magnet, or perhaps small neodymium magnets) in mind? Also what kind of solenoid size (diameter, length)?

I have a digitizing oscilloscope. I could set-up the arrangement that you specify and upload the signal on this website.

Joe and Stephen thank you for the replies.

Joe if I explain it a bit more clearly could I please take you up on your offer of your digitizing oscilloscope.

What we have been discussing at school is a solenoid (say 4cm diameter) connected to a galvanometer and a standard bar magnet (say 1cm wide and 6 cm long). The magnet approaches the solenoid a speed of say 1cm/s.

We understand that as the magnet approaches the solenoid the EMF in the solenoid increases. However we are curious to know what happens when the pole of the magnet enters the solenoid, up to when it gets to halfway through the solenoid. Does the EMF keep increasing, does it stay the same, does it decrease or does something else happen?

Whatever the effect could it be explained by looking at the orientation of the magnetic field lines as they leave the magnet. What I mean by this is at the poles the magnetic field lines are almost coming straight out of the bar magnet, so as it approaches the solenoid the majority of the field lines are roughly parallel to the length solenoid. However as you move from the end of a bar magnet towards to middle the field lines now start to be almost perpendicular to the length of the magnet. Therefore when the magnet enters the solenoid, the field lines are now perpendicular to the length of the solenoid.

Sorry about such a large post but it is hard to describe this without a diagram.

John,
I've dropped a bar magnet through a solenoid and recorded the induced emf on a digital oscilloscope. The dimensions are close to those that you mentioned (1 cm wide bar magnet and 4 cm diameter solenoid). You can download the results under "Motors and Generators downloads" link on the right hand side of this page.

Further details are given in the document.