How much force does a solenoid really have?

Force from a solenoid = \$(N\cdot I)^2 \dfrac{μ_0\cdot A}{(2 g^2)}\$

Where:

• μ0 = 4π×10-7
• F is the force in Newtons
• N is the number of turns of the coil
• I is the current in Amps in the coil
• A is the area in length units squared (cross sectional area of the coil)
• g is the length of the gap between the coil and the iron.

If you want to check your solenoids pull force and you know the number of turns and have a good estimate of the "gap" and the cross sectional area of the winding then use the formula.

However, it's notable that force is proportional to current-squared and if the 12V you used dropped down to (say) 6V under the load of the solenoid, the pull force would quarter because the current would have halved. It's also worth noting that the force is inversely proportional to the gap-squared - double the gap and the force quarters.

As you have noted, the 9v batteries you are using are drained with no load (14v for 2 equals 7v for a single 9v, which is ~1.15v for each of the alkaline cells inside a 9v battery). At load, it drops significantly. This is because two reasons. One, your solenoid has a large inrush and holding current. At 150% the typical voltage of 12v, there is larger current pull as well.

But Two, 9v batteries are NOT designed for large current draws. They are designed for long life at small currents (like smoke detectors). 9v batteries are typically mde up of 6 small packs of akaline cells in series. The typical capacity of a 9v is ~200 maH (This might be wrong, ill correct it later). As each cell is drained (simultaniously), the inernal resistance rises, the voltage lowers, and the current it can source does as well. A common solenoid will drain a 9v battery quickly. Other common consumer batteries have much higher capacity, and can withstand larger current drains for longer without too much voltage droop. AA batteries have current capacities of 2000maH, or 2 AH. C and D even more. 6v Lantern Batteries as well. Then there are the rechargeable batteries like 12v SLAs or LiPos, all that regularly power high drain motors for hours.

Think of it like this. Portable radios all use multiple D batteries in series. The only time you see a 9v in a radio is as a memory backup battery. Ditch the 9v Batteries, they are not useful for testing motors or solenoids beyond simply seeing if they are working.