For any point on or outside a spherical charged conductor at distance $r$ from the centre:

$$E = \frac{1}{4\pi\varepsilon_0}\frac{q}{r^2} \quad \text{and} \quad V = \frac{1}{4\pi\varepsilon_0}\frac{q}{r}$$

Taking the ratio of $V$ and $E$:

$$V = E \times r$$

Given:

• $E = 10\,\text{V/m}$
• $r = 20\,\text{cm} = 0.20\,\text{m}$

$$V = 10\,\text{V/m} \times 0.20\,\text{m} = 2.0\,\text{V}$$

Copper is a metal (conductor) with an infinite dielectric constant ($K \to \infty$).

The capacitance of a parallel plate capacitor with a slab of thickness $b$ and dielectric constant $K$ is:

$$C = \frac{\varepsilon_0 A}{d - b + \frac{b}{K}}$$

For a metallic conductor like copper, $K \to \infty$, which gives $\frac{b}{K} \to 0$:

$$C = \frac{\varepsilon_0 A}{d - b}$$

The effective separation between the capacitor plates is reduced from $d$ to $(d - b)$. Hence, option 2 is the correct answer.

When an electric dipole of dipole moment $\vec{p}$ is placed at an angle $\theta$ to a uniform electric field $\vec{E}$, the forces on $+q$ and $-q$ are equal in magnitude and opposite in direction ($+q\vec{E}$ and $-q\vec{E}$).

The net force is zero, but these parallel opposite forces form a couple producing a torque:

$$\tau = p E \sin\theta$$

In vector cross product notation:

$$\vec{\tau} = \vec{p} \times \vec{E}$$