Consider the situation shown. A conducting rod is
moving with uniform velocity v to the right in a uniform magnetic field B
pointing into the plane of the paper. Let the length of the rod be L.
Here the electrons of the rod which otherwise have no net velocity have the velocity v due to the motion of the rod. Therefore, the magnetic field exerts a force given by
Here the electrons of the rod which otherwise have no net velocity have the velocity v due to the motion of the rod. Therefore, the magnetic field exerts a force given by
F
= q (v× B) = -e (v× B)
, towards point B. As a result a negative
polarity at the lower and positive polarity at the upper end of the rod starts appearing,
generating an electric field E in the downward direction. Now, the electrons start
experiencing two forces :-
(1)by the electric field in the upward direction given by F= qE = -eE
(2) by the magnetic field in the downward direction given by F = -e (v× B).
(1)by the electric field in the upward direction given by F= qE = -eE
(2) by the magnetic field in the downward direction given by F = -e (v× B).
Since initially electric field is weak and therefore resultant
force on the electrons will be downwards, accumulating more electrons and therefore
the electric field keep becoming stronger and stronger. At one point of time,
the electric force would become strong
enough so that electron flow is halted. Under such condition,
F= qE = -eE = F = -e (v× B)
Or
-eE = -e (v× B)
Or
E = Bv sin θ
As electric potential difference, V=EL and here, sin θ
= sin 900 = 1
Therefore,
emf induced due to motion of the rod (motional emf) = BLv
Motional emf in a conducting rod :- The electric field in the metal bar causes a potential difference , EL = BLv.
Since the circuit is complete causing a current to flow in counter-clockwise direction. The moving current tends to oppose the motion of rod towards right (Lenz law) thus force is exerted on the rod towards left against which work must be done which would be ultimately converted to electric energy.
Related Concepts :-
Motional emf in a conducting rod :- The electric field in the metal bar causes a potential difference , EL = BLv.
Since the circuit is complete causing a current to flow in counter-clockwise direction. The moving current tends to oppose the motion of rod towards right (Lenz law) thus force is exerted on the rod towards left against which work must be done which would be ultimately converted to electric energy.
Related Concepts :-
