Radius=a
Charge=Q
V=∫dq4πϵ0rV=\smallint \frac{dq}{4 \pi\epsilon_0 r}V=∫4πϵ0rdq
dq=λdldq=\lambda dldq=λdl
dl=adθdl=ad\thetadl=adθ
λ=θπa\lambda=\frac{\theta}{\pi a}λ=πaθ
dq=θπa(adθ)dq=\frac{\theta}{\pi a} (ad\theta)dq=πaθ(adθ)
dq=θdθπdq=\frac{\theta d\theta}{\pi}dq=πθdθ
Limit
θ=0°\theta=0°θ=0° to θ=π\theta=\piθ=π
V=14πϵ0∫dqaV=\frac{1}{4\pi\epsilon_0}\int\frac{dq}{a}V=4πϵ01∫adq
V=14πϵ0∫0πQdθπaV=\frac{1}{4\pi\epsilon_0}\smallint _{0}^ \pi \frac{Q d\theta}{\pi a}V=4πϵ01∫0ππaQdθ
V=Q4πϵ0aV=\frac{Q}{4 \pi\epsilon_0 a}V=4πϵ0aQ
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