# Force On A Current Carrying Conductor

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__ Force on a Current Carrying Conductor: __A conductor has free electrons which can move in the presence of a field. Since a magnetic field exerts a force on a charge moving with a velocity , it also exerts a force on a conductor carrying a current.

Consider a conducting wire carrying a current . The current density at any point in the wire is given by'

where is the number density of electrons having a charge each and is the average drift velocity at that point.

Consider a section of length of the wire. If is the cross sectional area of the section oriented perpendicular to the direction of , the force on the electrons in this section is

where is the amount of charge in the section

Thus the force on the conductor in this section is

If represents a vector whose magnitude is the length of the segment and whose direction is along the direction of , we may rewrite the above as

The net force on the conductor is given by summing over all the length elements. If denotes a unit vector in the direction of the current, then