The linear charge density on a dielectric ring of radius R is varying with θ as λ=λ0 cos θ2 where λ0 is a constant. If the potential at the centre O of the ring (in volt) is 10-x, find the value of x.

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The linear charge density on a dielectric ring of radius R is varying with $θ a s λ = λ_{0} \cos \frac{θ}{2}$ where $λ_{0}$ is a constant. If the potential at the centre O of the ring (in volt) is $10 - x$ , find the value of x.

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answer is 10.

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Potential is a scalar quantity. The charge density function suggests that net charge is zero . Net charge on the ring

$Q= \int_{0}^{2π} λR dθ = λ_{0} R \int_{0}^{2 π} \cos (θ / 2) d θ = 0 V = \frac{1}{4 π ε_{0}} (\frac{Q}{R}) = 0$

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