Does a difference in magnetic field make the electrons move and make electric current flow,how? I have seen a sentence written in my textbook,"Current is produced in a conductor when it is moved through a magnetic field because the magnetic lines of force are applying a force on the free electrons in the conductor and causing them to move"Is it true?if this is true,then why does electrons not move when the conductor is kept stationary inside the magnetic field of the magnet,can someone tell me more details about this?this was written in the explanation of as to why difference in magnetic field or strength makes electric current flow through the conductor which is inside the influence of the magnet.Can someone tell how?how is it possible?why does it happen?I'm a 10th grade student so please use as simple words and terms as possible
 A: 
Current is produced in a conductor when it is moved through a magnetic field because the magnetic lines of force are applying a force on the free electrons in the conductor and causing them to move"

That sentence is oversimplified and misleading.
First of all, magnetic fields do not attract electrons or charges. It's not that so forget about that.
But what is true is that:

*

*A changing magnetic field does exert a force on charges such as electrons

*Moving charges do have a force exerted on them by a magnetic field,
even an unchanging (static) magnetic field.

When you think about it, the two are kind of the same thing. If a charge is moving through a magnetic field, whether or not the magnetic field is changing dynamic) or unchanging (static) there is relative motion between the magnetic field and the charge. If the charge is just sitting there and the magnetic field is changing, there's relative motion of a sort between the charge and magnetic field.
Generators work this way: They swing a wire (which contains electrons) through a magnetic field. This qualifies as moving electrons through a magnetic field. If you orient the wire properly in the magnetic field as you swing it, a force is applied to the electrons are pushed in the direction along the length of the wire producing voltage, and if the wire is connected in a circuit then the electrons can move out of the wire producing current.
Old CRT monitors also work this way: Electrons are fired at right angles to the lines of a magnetic field and the magnetic field exerts a force 90 degrees (orthogonal) to both the magnetic field lines and the motion of the electron to steer the electron. Everything is 90 degrees to each other so the directions of the motion and forces are quite unlike anything you are accustomed to encountering in every day life. It will take some time to get used to.
So I repeat: magnetic fields do not attract or repel electrons (if they did, then electrons would have a force applied to them in the same direction as the the lines of a magnetic field, but they do not. It's 90 degrees to it and only if the electrons is moving or the magnetic field is changing).
ADDITION:
Was that description of directions confusing? I'm sure it was without pictures and even the pictures are confusing sometimes.

*

*Imagine shooting a bullet (the electron/charge) horizontally in a room with no gravity.

*If the room is dark (no magnetic field), the bullet just travels straight.

*If there are lights (the magnetic field) on the floor shining up, or lights on the ceiling shining down, the bullet wants to curve left depending on the direction the light is shining as the bullet passes through.

*The bullet actually continually veers left or right to make an arc as it travels since when the bullet veers to one side, it is no longer traveling straight in the initial direction. It is traveling in a slightly different direction and then a force is applied to the left or right of that. This happens continuously so it forms an arc.

*If the bullet is just sitting there no force is exerted whether or not there are lights. A force is only exerted on the bullet is there are lights and the bullet is moving.

*If the lights are changing in brightness, a force is exerted on the bullet even if it was initially sitting there.

This is why those images you see in particle accelerator photos have arcs all over the place. In this image the charges are  moving left to right, and the magnetic field is either pointing into the page or out of the page.

https://discover.hubpages.com/education/A-Guide-to-Subatomic-Particles
A: Yes. It is called the magnetic interaction force force of the of the Lorentz equation:
$$F_{(M)}=q(\mathbf{v} \times \mathbf{B})$$
Sometimes it is also referred as Laplace force for parallel electric wires.
