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Magnetic force is a consequence of electromagnetic force and is caused due to the motion of charges. We have learned that moving charges surround itself with a magnetic field. With this context, the magnetic force can be described as a force that arises due to interacting magnetic fields.
Magnetic force can be defined as:
The magnetic force between two moving charges may be described as the effect exerted upon either charge by a magnetic field created by the other.
The magnitude of the magnetic force depends on how much charge is in how much motion in each of the objects and how far apart they are.
Mathematically, we can write magnetic force as:
This force is termed as the Lorentz Force. It is the combination of the electric and magnetic force on a point charge due to electromagnetic fields. The interaction between the electric field and the magnetic field has the following features:
Let us now discuss the force due to the magnetic field in a straight current-carrying rod.
Then the total number of charge carriers can be given by nAI, where I is the steady current in the rod. The drift velocity of each mobile carrier is assumed to be given as vd. When the conducting rod is placed in an external magnetic field of magnitude B, the force applied on the mobile charges or the electrons can be given as:
F=(nAI)qvd × B
Where q is the value of charge on the mobile carrier.
As nqvd is also the current density j and A×|nqvd| is the current I through the conductor, then we can write:
F=[(nqevd)AI] × B = [jAI] × B=Il × B
Where I is the vector of magnitude equal to the length of the conducting rod.