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The linear charge density on the circumference of a circle of radius 'a' varies as λ = λ₀cosθ. The total charge on it is _____(A) zero (B) infinite (C) πaλ₀ (D) 2πa |
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Answer» Total charge will be zero. Explanation:DQ = ʎ dx Now do the DIFFERENTIATION for above equation, ƪ dq = ƪ ʎ dx Q = ʎᵒ ƪ cos Ɵ . dx [ Ɵ = Arc/radius d Ɵ = dx/R so dx = RdƟ] q = ʎᵒ 0ƪ2π cos Ɵ . dƟ = ʎᵒ R . [Sin Ɵ]2π = ʎᵒ R [ Sin 2π – Sin Ɵ] q = ʎᵒ R [ 0 – 0] So total charge, q = 0 |
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