A non-conducting rod of length ℓ , mass m and linear charge density λ is hinged at one end. It is kept in horizontal position in vertical plane in front of a current carrying wire as shown in figure.

Question

A non-conducting rod of length ℓ , mass m and linear charge density λ is hinged at one end. It is kept in horizontal position in vertical plane in front of a current carrying wire as shown in figure. The system is released from horizontal position. The angular velocity of the rod when it makes angle 30° with the horizontal is ω and magnetic force on the rod at that instant is F, then :-

TestHub · Accepted Answer

M g 4 ℓ ​ ⇒ ω ∫ df ⇒ F ​ = 2 1 ​ 3 m ℓ 2 ​ ω 2 = 2 ℓ 3 g ​ ​ = ∫ 0 ℓ ​ ( λ d x ) ( ω x ) 2 π x sin 3 0 ∘ μ 0 ​ i ​ = π λω μ 0 ​ i ​ ℓ = λ 2 ℓ 3 g ​ ​ π μ 0 ​ i ℓ ​ ​

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