IPhO 2007, Теория — Задача 1.3

• 3.1 $V_S = V\,\frac{\frac{2\varepsilon_0 A x}{d^2 - x^2}}{C_S + \frac{2\varepsilon_0 A d}{d^2 - x^2}}$
• 3.2 $V_S = V\,\frac{2\varepsilon_0 A x}{d^2 C_S + 2\varepsilon_0 A d}$

3.1)

Starting with Kirchhoff’s laws, for two electrical circuits, we have

(Each has (0.3), Note: the sings may depend on the specific choice made)

Noting that $V_s = \frac{Q_S}{C_S}$ one obtains

((0.4) + (0.2): (0.4) for solving the above equations and (0.2) for final result)

Note: Students may simplify the above relation using the approximation $d^2 \gg x^2$. It does not matter in this section.

3.2)

Ignoring terms of order $x^2$ in the answer to 3.1., we get

(0.2)