Total Force Of Solenoid on Surrounding Ions

How would you calculate the total force that a solenoid would expert on surrounding ions (ionized air for example)?

My best guess was to find the force for one singular ion and multiply it by the number of ions within reach of the solenoid but I got a value that was too high to be accurate. The only reason I could think of is that I multiplied by the wrong number of ions.

Assuming the above approach was correct,

An example calculation:

F = (q * v * B * sin(theta) * number of ions in vicinity) = (1.6 * 10^-19 C) * 300 m/s * 0.8T * sin(90) * 10^24 ions

• I took the charge of an electron
• Average molecular velocity of air molecules is around 300 m/s
• I’m only calculating for ions that are passing perpendicular to the solenoid for sake of simplicity.
• I found that on average there are 10^26 air molecules per cubic meter of space and suppose only 1% ended up getting ionized.

What’d I miss, assuming this approach was correct to use?