For metals the value of dielectric constant `(K)` is

Options

A. zero
B. infinite
C. 1
D. 10

Explanation

To determine the value of the dielectric constant \( K \) for metals, we can follow these steps:

### Step 1: Understand the Definition of Dielectric Constant
The dielectric constant \( K \) is defined as the ratio of the permittivity of a medium (\( \varepsilon \)) to the permittivity of free space (\( \varepsilon_0 \)). Mathematically, it is expressed as:
\[ K = \frac{\varepsilon}{\varepsilon_0} \]

### Step 2: Identify the Permittivity of Vacuum
The permittivity of free space (vacuum) is a constant value, denoted as \( \varepsilon_0 \). For vacuum, the dielectric constant \( K \) is defined as:
\[ K_{\text{vacuum}} = 1 \]

### Step 3: Understand the Behavior of Metals
Metals are excellent conductors of electricity and have a high density of free charge carriers (electrons). When an external electric field is applied to a metal, these free charges move in response to the field, leading to a significant polarization effect.

### Step 4: Analyze the Polarization in Metals
In metals, the free electrons can move almost freely, which means that they can completely shield the electric field within the metal. This results in a very high effective permittivity for the metal.

### Step 5: Conclude the Value of Dielectric Constant for Metals
Since the permittivity of the metal (\( \varepsilon \)) becomes very large due to the complete polarization, we can conclude that:
\[ K = \frac{\varepsilon}{\varepsilon_0} \rightarrow \infty \]
Thus, the dielectric constant \( K \) for metals is considered to be infinite.

### Final Answer
The value of dielectric constant \( K \) for metals is infinite.

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