Question

A wire of length L is placed in a magnetic field B, If the current in the wire is I, then maximum magnetic force on the wire is

Answer 1

Answer:

F = BIL

Explanation:

We know thatmagnetic force(F) acting on the wire of length (L) carrying current (I) placed in a magnetic field (B) is   $I(L\times B)$.

i.e. $F = ILB\sin(\theta)$...(1)

Now the force (F) is maximum when the value $\sin(\theta)$ is maximum.

i.e. when $\theta = 90\deg$ then  $\sin(\theta = 90 \deg) = 1$

Therefore equation (1) becomes F = BIL.

Hence, the maximum magnetic force acts on the wire is F = BIL.

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Answer 2

Answer:

The force on a section of wire of length L carrying a current I through a magnetic field B is

F = I (L × B)

F= ILB sin θ, where θ is angle between wire and magnetic field.

Explanation:

Using the principle of force on a moving charge, apply force to the conductor carrying the current:-

• Consider a metallic conductor with cross-sectional area A and length L that is positioned at an angle θ to the direction of a uniform magnetic field B.
• The conductor is carrying current I.
• According to the free-electron concept of metals, current in metals is caused by the mobility of free electrons.
• Everyfree-electron feels a force from a magnetic field when it is put in a conductor.
• The net force exerted on the conductor is the total of all forces acting on all electrons.
• If $v_{d}$represents the drift speed of free electrons, then

Current I = $neAv_{d}$    ....(i)

In this equation, n denotes the number of free electrons per unit volume.

Magnetic force on each electron = $av_{d}Bsin$θ    ....(ii)

Its direction is perpendicular to both  $v_{d}$ and $B$

The volume of the conductor $V= AL$

∴ The total number of free electrons in the conductor = $nAL$

Net magnetic force on each conductor

F= ( force on one electron) × ( number of electron)

$F= ev_{o} B sin$θ × $nAL$

$F= (neAv_{o}).BLsin$θ

Using equation (i)

$F= ILBsin$θ

Force will be maximum when $sin$θ $= 1$ or θ =90°

That is when the length of the conductor is perpendicular to the magnetic field.

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