At the centre of a half ring of radius $$R = 10$$ cm and linear charge density $$4$$ nCm$$^{-1}$$, the potential is $$x\pi$$ V. The value of $$x$$ is _______

For a half ring of radius $$R$$ with linear charge density $$\lambda$$, the total charge is $$Q = \lambda \pi R$$. Since every element is at distance $$R$$ from the centre, the potential is:

$$V = \frac{1}{4\pi\epsilon_0} \cdot \frac{Q}{R} = \frac{1}{4\pi\epsilon_0} \cdot \frac{\lambda \pi R}{R} = k\lambda\pi$$

where $$k = 9 \times 10^9$$ N m$$^2$$/C$$^2$$.

The linear charge density is $$\lambda = 4$$ nC/m = $$4 \times 10^{-9}$$ C/m.

Substituting these values gives

$$V = 9 \times 10^9 \times 4 \times 10^{-9} \times \pi = 36\pi \text{ V}$$

Hence, $$x = \boxed{36}$$.