Mostly positive charge on the wire is because of protons which are containing nucleus. When the protons are not in motion the force acting on them will be zero. So charge will be zero. But there is a negative charge too. Negative charge is due to electrons.

Formula used:

Where F is magnetic force

q is electric charge =

v is velocity

B is magnetic field

is angle between magnetic field and a charge

So when the electrons are in motion the wire will carry current. Magnetic force will act on the wire. That’s why magnetic field exerts a force on the wire.