# Magnetic field between two solenoids

## Main Question or Discussion Point

Say if I have two identical solenoids with equal number of turn etcs.. and I connect them in series such that their magnetic field add up. (instead of canceling each other)

What would be the magnetic field between them? If magnetic field due to one solenoid is B=u0IN/l, then is the magnetic field 2x that B value? (My reasoning is that the magnetic field lines from each solenoid adds up)

Thanks.

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the formula you are using:

$$B = \mu_o nI$$

is an approximation that the magnetic field inside a solenoid is constant at all points and zero everywhere else. This approximation holds good for quite a many applications.

when you connect two solenoids, you have the same 'n' [as u said].. i.e the same number of turns per unit length. Since they are in series.. the current flow will be same through them in both cases i.e. connected one at a time or both at a time. This however assumes that the resistance of the solenoid is 0. $\mu_o$ is purely a property of the material in which the field propagates, which will be the same in both the cases i.e. Air.

so.. all things considered, the magnetic field will remain same inside the solenoid. However your approximation will work better in case of the two solenoids since this approximation depends on the fact that the solenoid be long. This however is valid only if there is no gap between those two solenoids i.e. they are connected one after the other without any leads between them.

Oh that make sense. thanks