Question

derive expression for the force acting on a closed circuit in a uniform magnetic field ​

Answer 1

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.