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[ Grade 12 Physics ]
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Explanation:
a wire of length L and linear charge density is λ = Kx
we know,
linear charge density means charge per unit length.
so, we can say, λ = dQ/dx
⇒ dQ = λ.dx
⇒ ∫dQ = ∫Kx.dx [∵ λ = Kx ]
⇒
⇒ Q = KL²/2
now, according to Gaussian theorem,
Ф = Q/ε₀
here, Ф is electric flux, Q is net charge inclosed in Gaussian surface and ε₀ is permitivity of medium [vaccum]
so, Ф = KL²/2ε₀
flux through s1=Q/ε₀
flux through s2=[Q+[1/2]kl^2]/ε₀
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