- #1

yucheng

- 232

- 57

- Homework Statement
- N/A

- Relevant Equations
- N/A

So I have a ring(red) of uniform charge ##\lambda## per unit length, and I want to calculate the electric potential at the origin (actually on any point of the ring). It is clear that the ring is given by the equation $$r=2 R \sin \theta$$, in polar coordinates, where R is the radius of the ring. Since potential is given by $$V = \frac{1}{4 \pi \epsilon_0} \int \frac{dq}{r}$$, and $$dq = d\ell \lambda$$, but $$d\ell = \sqrt{(\frac{dr}{d\theta})^2 + r^2} d\theta = 2R d\theta$$. Therefore, $$V = \frac{1}{4 \pi \epsilon_0} \int \frac{d\ell \lambda}{r} = \frac{1}{4 \pi \epsilon_0} \int^{\pi}_{0} \frac{2R\lambda}{2R \sin \theta} d\theta = \frac{1}{4 \pi \epsilon_0} \lambda \int^{\pi}_{0} \frac{1}{\sin \theta} d\theta$$, which does not converge... what's wrong?

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