:O) Desive the ex pression for
for the magnetic force acting
Carrying
straight conductor placed in a uniform magnetic field
and express in it vector form
Answers
Explanation:
Force on current carrying conductor on the basis of force on a moving charge. Consider a metallic conductor of length L, cross- sectional area A placed in a uniform magnetic field B and its length makes an angle θ with the direction of magnetic field B. The current in the conductor is I.
According to free electron model of metals, the current in a metal is due to the motion of free electrons. When a conductor is placed in a magnetic field, the magnetic field exerts a force on every free-electron. The sum of forces acting on all electrons in the net force acting on the conductor. If vd is the drift velocity of free electrons, then
Current I=neAv
d
....(i)
Where n is number of free electrons per unit volume.
Magnetic force on each electron =av
d
Bsinθ ....(ii)
Its direction is perpendicular to both
v
d and
B
Volume of conductor V=AL
Therefore, the total number of free electrons in the conductor =nAL
Net magnetic force on each conductor
F= ( force on one electron) × ( number of electrons)
=(ev
0
Bsinθ).(nAL)=(neAv
0
).BLsinθ
Using equation (i) F=IBLsinθ .....(iii)
∴F=ILBsinθ
This is the general formula for the force acting on a current carrying conductor.
In vector form
F
=
I
L×
B
.....(iv)
Force will be maximum when sinθ=1 or θ=90
o
. That is when length of conductor is perpendicular to magnetic field.
Hope this answer is helpful for you.
Answer: Force on current carrying conductor on the basis of force on a moving charge. Consider a metallic conductor of length L, cross- sectional area A placed in a uniform magnetic field B and its length makes an angle θ with the direction of magnetic field B. The current in the conductor is I.
According to free electron model of metals, the current in a metal is due to the motion of free electrons. When a conductor is placed in a magnetic field, the magnetic field exerts a force on every free-electron. The sum of forces acting on all electrons in the net force acting on the conductor. If vd is the drift velocity of free electrons, then
Current I=neAv
d
....(i)
Where n is number of free electrons per unit volume.
Magnetic force on each electron =av
d
Bsinθ ....(ii)
Its direction is perpendicular to both
v
d and
B
Volume of conductor V=AL
Therefore, the total number of free electrons in the conductor =nAL
Net magnetic force on each conductor
F= ( force on one electron) × ( number of electrons)
=(ev
0
Bsinθ).(nAL)=(neAv
0
).BLsinθ
Using equation (i) F=IBLsinθ .....(iii)
∴F=ILBsinθ
This is the general formula for the force acting on a current carrying conductor.
In vector form
F
=
I
L×
B
.....(iv)
Force will be maximum when sinθ=1 or θ=90
o
. That is when length of conductor is perpendicular to magnetic field.