CBSE Class 12 · 2017 · Magnetic Effects of CurrentShort Answer

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State Lorentz's force and express it in vector form. Which pair of vectors are always perpendicular to each other? Derive the expression for the force acting on a current-carrying conductor of length

L

in a uniform magnetic field

B

Solution

The magnetic force on a charge is

F = q (v \times B)

; it is always perpendicular to

v

(and to

B

). For a conductor of length

L

, area

A

, carrying current

I

with electron number density

n

and drift velocity

v_{d}

, the total charge in it is

q = n A L

, and

I = n A v_{d} q_{e}

. Summing the force on all carriers:

F = (n A L) q_{e} (v_{d} \times B) = I L \times B,

where

L

points along the current. Its magnitude is

F = B I L sin θ

CBSE Class 12 Board · 2017 · Subjective

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