QJEEM19Phe93e: JEE Main 2019 Physics - Class 12 JEEM19Phe93e Solution: An insulating thin rod of length l has a linear charge density…

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QJEEM19Phe93e: JEE Main 2019 Physics - Class 12 JEEM19Phe93e Solution: An insulating thin rod of length l has a linear charge density…

An insulating thin rod of length

l

has a linear charge density

ρ (x)

=

ρ_{0} \frac{x}{l}

on it. The rod is rotated about an axis passing through the origin (x = 0) and perpendicular to the rod. If the rod makes n rotations per second, then the time averaged magnetic moment of the rod is -

Multiple Choice Options

A π3nρl3
B π4nρl3
C nρl3
D πnρl3

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Accepted Answer

∵

M = NIA

dq =

λ

dx & A =

π

x²

\int d m = \int (x) \frac{ρ_{0} x}{ℓ} d x . π x^{2}

M =

\frac{n ρ_{0} π}{ℓ} . \int_{0}^{ℓ} x^{3} . d x = \frac{n ρ_{0} π}{ℓ} . [\frac{L^{4}}{4}]

M =

\frac{n ρ_{0} π ℓ^{3}}{4}

or

\frac{π}{4} n ρ ℓ^{3}

QJEEM19Phe93e: JEE Main 2019 Physics - Class 12 JEEM19Phe93e Solution: An insulating thin rod of length l has a linear charge density…

Multiple Choice Options

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