Question

derive the expression of force​

Answer 1

Answer:

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.

Answer 2

Answer:

Let initial momentum ($p_i$) be mu

Let final momentum ($p_f$) be mv

According to 2nd law of motion

$\frac{p_f - p_i}{t} \propto \: f$

$\implies \: f \propto \frac{mv \: - mu}{t}$

$\implies \: f \propto \frac{m(v - u)}{t}$

$f \propto \: ma \: \: \: \: \: \: ( \frac{v - u}{t } = a )$

To remove the proportionality sign. We would add k as the proportionality constant

$f = kma \\ f = ma \:$

because by the definition of force k = 1