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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