# Relation between Voltage and EMF of a solenoid

I've been working an a senior design project for school that uses solenoids, I needed to characterize the solenoids since they came from china and didn't have a datasheet. One of the tests that I conducted was to find push force vs. Voltage and Current.

Test setup: I positioned a solenoid over a digital scale using a rig that I built. I know this wasn't the best way to go about this but i just wanted a rough idea of the push force. I then connected the solenoid to a power supply that can limit both voltage and current. I started at $3V$ and $100mA$ and incremented the current up to $600mA$. Then I increased the voltage by $1V$ and repeated, i did this all the way up to $12V$.

Results:

This graph seems to show that there is a linear increase in push force with current up to a certain point. This would make sense if we assume the push force is related to magnetic field (which i think it should be). The equation for the magnetic field generated by a coil is $B =\mu_0\frac{NI}{L}$ so as $I$ increases $B$ increases, that makes sense. What im confused about is why does the force level off after a certain point, and why does this level off point seem to be controlled by the voltage. My best guess would be that this has something to do with the magnetic Flux, where the magnetic field can increase up to a certain point given the electric field created by the voltage, as you increase voltage this moves the upper limit of the magnetic field density. However I cant back this up with any numerical proof cause the math is a little beyond my pay grade.

• The title of the question is misleading, 'emf' is usually a shorthand for electromotive force (force acting on charge carriers), whereas the question asks about ponderomotive force (force acting on the whole body). – Ján Lalinský Jul 1 '18 at 18:01

If your power supply had no current-limiting facility, the current through the electromagnet would be proportional to the voltage applied (Ohm's law). Now take the case of one of the lines on your graph – I'll go for the 4 V line. As you increase the setting of your current-limiter, the current increases, but beyond about 300 mA, it's not the setting of the current-limiter which controls the current but the applied voltage. I'd guess that the resistance of the solenoid is about 13 ohm, so with a voltage of 4 V the current can never exceed $I=\frac{4\ V}{13\ \Omega}= 0.3 A$. That's why, beyond the 300 mA setting of your current-limiter, the force hardly changes; the current doesn't change!