Practice portal › Electric Charge and Properties › Field of Continuous Charge Distributions
Asked in GSEB Board July 2016 · Ring, arc and disc
Given: λ = λ₀ cos θ on a circle of radius a.
Idea: add up dq = λ dl round the circle, with dl = a dθ.
Q = ∫₀^2πλ₀ cos θ a dθ = aλ₀[sin θ]₀^2π
Q = aλ₀(sin 2π - sin 0) = 0
The half of the ring where cos θ > 0 carries positive charge, and the other half carries an equal negative charge.
So the total charge is zero.
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