How does a magnetic field induce an electric current?

[Biker]

Trying to understand how a magnetic field induces an electric current

Suppose you have a wire in the magnetic field like this:

If you move the wire with a velocity of V to the left. Then the magnetic field should exert a force on the wire which ultimately on the charges in the wire. According to the right hand rule, It should be to the top of the page.

From what I learned particles in magnetic field move in circular or spiral path ( not sure if there is more).. So let's go back to our case. The charges should have a circular path not in a straight line. So how is a current produced with a circular motion moving charges?

 

[sophiecentaur]

There are many diagrams about this (http://www.electrical4u.com/fleming-left-hand-rule-and-fleming-right-hand-rule/).

Then the magnetic field should exert a force on the wire which ultimately on the charges in the wire.

This is the wrong way round, actually. The movement and the field primarily cause the charges to be deflected. Because the wire is the only path they can take, they go in a straight line but they would move on a circular path if they were free to move.
The Eddy Currents that occur when an alternating field is applied to a metal (saucepan over an induction hob, for instance) do actually go in circular paths. In most other instances, this is a disadvantage and lumps of metal are often split up into laminations to suppress the formation of these eddy currents.