The linear charge density on a dielectric ring of radius r is varying with θ as , where λ0 is 5 C/m. Find the potential at the centre O of ring. [in volt]
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The linear charge density λ varies with angle θ as λ = λ₀ cos(θ/2). To find the electric potential at the center, we integrate contributions from all charge elements dq = λ dl = λ (r dθ) around the ring. The potential dV from each element is dV = (1/(4πε₀)) (dq/r).
Thus, total potential V = (1/(4πε₀)) ∫(λ dθ) from 0 to 2π = (1/(4πε₀)) ∫[λ₀ cos(θ/2) dθ].
Solving the integral: ∫cos(θ/2) dθ = 2 sin(θ/2). Evaluating from 0 to 2π gives 2[sin(π) - sin(0)] = 0.
Therefore, the net potential at the center is zero.
Final Answer: 0