Question

The net charge in a current-carrying wire is zero. Then, why does a magnetic field exert a force on it?

Answer 1

The net charge in a current- carrying wire is zero. Yet, negative charge, i.e. electrons are moving in the wire towards the positive terminal. It is this motion of electrons in the conductor which produces the current in the wire and is also responsible for the magnetic force acting on the wire.

F = qVBsin($\theta$), where F is the force, q is the charge of electrons, V is the velocity of electrons and B is the magnetic field.

Moreover, the positive charges on the wire are due to nucleus containing proton. As they are not moving so there is no force on them, so the force is only due to the moving electrons in the wire.