Why a force is exerted on a current carrying conductor in an externel magnetic field?

Question

Why a force is exerted on a current carrying conductor in an externel magnetic field?

Answer 1

Remember the equation:

F = qv x B

This allows you to calculate the magnitude of the force on a particle moving in an external magnetic field.  It's the cross product of charge times velocity with the external magnetic field.

Well, knowing this much, I will answer your question with another question: What is current but moving charge?  We use a similar equation to find the force on a "current-carrying conductor":  F = iL x B

This is just a macroscopic version of F = qv x B.  

As an example, think of your conductor as having positive charges moving along the x axis and negative charges moving the opposite direction along the x axis (you can draw this out on paper).  

Now imagine an applied B field along the +y axis.  By F = qv x B, we have a net force coming OUT of the paper on each moving proton (remember to use the right-hand rule).  

Additionally, the right hand rule gives us a net force coming OUT of the paper on each moving electron, even though the protons and electrons are moving in opposite directions. (this is due to the negative value of q in the cross product).

Answer 2

Current is the quantity that both produces and responds to magnetic fields, just as charge is the quantity that both produces and responds to electric fields and mass is the quantity that both produces and responds to gravity.

Answer 3

The Magnitude of the Force is given by

F=BIL

       Where       F is the force on the conductor in Newtons

                          B is the Magnetic Flux Density in Tesla

                          I is the current in Amperes.

                     l    L is the length of the conductor in metres.