We have seen that a magnetic field is associated with a current carrying conductor. If a current carrying conductor is placed in a magnetic field, it experiences a force (F) depending on the magnitude of current (I), length of conductor (l) and magnitude of the magnetic field (B). The mathematical expression for the force in vector form is given by F=I(lxB)
The above equation can be derived as follows: Consider a metal of length l, cross sectional area 'A' and free electron density 'n' carrying a current I. In metals the current conduction is due to the drifting of electrons. When the conductor is placed in a magnetic field of strength B, each of the moving electron in the metal experiences a Lorentz force given by F=eVdxB where Vd is the drift speed of electrons.
The drift speed of electrons is Vd=1/nAe
Therefore the force experienced by each electron is f=eVdBsin theta=e(1/nAe)B sin theta
f=IBsin theta/nA
As the conductor is of length l the number of free electron present is N=Aln
Therefore the total force acting on a conductor of length l is
F=Nf=Aln(IB sin theta)/nA=IlB sin theta
In vector form it can be written as F=I(lxB), here the direction of l is taken as the direction of I.
The above equation can be derived as follows: Consider a metal of length l, cross sectional area 'A' and free electron density 'n' carrying a current I. In metals the current conduction is due to the drifting of electrons. When the conductor is placed in a magnetic field of strength B, each of the moving electron in the metal experiences a Lorentz force given by F=eVdxB where Vd is the drift speed of electrons.
The drift speed of electrons is Vd=1/nAe
Therefore the force experienced by each electron is f=eVdBsin theta=e(1/nAe)B sin theta
f=IBsin theta/nA
As the conductor is of length l the number of free electron present is N=Aln
Therefore the total force acting on a conductor of length l is
F=Nf=Aln(IB sin theta)/nA=IlB sin theta
In vector form it can be written as F=I(lxB), here the direction of l is taken as the direction of I.
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| Rectangular Coil in a Magnetic Field |
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