The electric potential at the centre of two concentric half rings of radii $$R_1$$ and $$R_2$$, having same linear charge density $$\lambda$$ is

Potential due to a charged arc at its centre is

$$V=\frac{1}{4\pi\varepsilon_0}\int\frac{dq}{R}$$

Since RRR is constant for an arc,

$$V=\frac{1}{4\pi\varepsilon_0}\frac{Q}{R}$$

For a half ring of radius R, length is

$$\pi R$$

So charge on it is

$$\left(Q=\lambda(\pi R\right)$$

Thus potential due to one half ring:

$$V=\frac{1}{4\pi\varepsilon_0}\frac{\lambda\pi R}{R}$$

$$=\frac{\lambda\pi}{4\pi\varepsilon_0}$$​

$$=\frac{\lambda}{4\varepsilon_0}$$

Interesting result: it is independent of radius.

So each half ring contributes

$$\frac{\lambda}{4\varepsilon_0}​$$

For two concentric half rings, potentials add:

$$V=\frac{\lambda}{4\varepsilon_0}+\frac{\lambda}{4\varepsilon_0}$$

$$V=\frac{\lambda}{2\varepsilon_0}$$