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A non-conducting rod of length L with linear charge density λ = λ 0 x where x is the distance from end A is rotating with constant angular speed ω about the same end. If the angular velocity of the rod ( ω ) is large, then the magnetic dipole moment of the system is ω λ 0 L 4 n . What is the value of n ?

Correct answer

8

Step-by-step solution

d q = λ 0 x d x ⇒ i = ω λ 0 x d x 2 π d m = ω λ 0 x d x 2 π π x 2 ⇒ m = ∫ d m = ∫ ω λ 0 2 x 3 d x ∴ m = ω λ 0 L 4 8 n   =   8

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