Force Experienced by a Current Carrying Conductor in a Uniform Magnetic Field

In a current carrying conductor, electron are moving opposite to the direction of current. Thus the electron will experience force from magnetic field but electrons are bounded, thus the conductor will experience force.

Force on the conductor

Let a metallic conductor having length ‘l’ and cross-sectional area ‘A’ carrying current ‘I’ is placed in a uniform magnetic field of strength ‘B’ as shown in figure.

∴Volume of conductor, V = Al

Let ‘n’ be the number of electrons per unit volume. Then:

$\text{n} = \frac{\text{N}}{ \text{V}}$

or, N=nV

∴ N=nAl ………(i)

Let ‘e’ and ‘v’ be the charge and drift velocity of each electron respectively.

∴ Lorentz force experienced by each electron, (F)=Bevsinθ

or, F=Nf
or, F=NBevsinθ
or, F=nalBevsinθ
or, F=B.venA.lsinθ
or, F=BIlsinθ

Vectorically, $ \vec F= I(  \vec v  \times  \vec B)$

Here, the direction of force is perpendicular  to the plane of l and B.

 

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