**Dielectric Constant of a Metal**

The dielectric constant, also known as the relative permittivity, is a property that characterizes the ability of a material to store electrical energy in an electric field. It is defined as the ratio of the electric field in vacuum to the electric field in the material. The dielectric constant of a material is always greater than or equal to one.

**Explanation:**

1. **Definition of Dielectric Constant:** The dielectric constant, denoted by the symbol ε (epsilon), is a dimensionless quantity that represents the electrical permittivity of a material compared to the permittivity of a vacuum. It is given by the equation ε = εr/ε0, where εr is the relative permittivity of the material and ε0 is the permittivity of vacuum.

2. **Dielectric Constant of a Metal:** Metals are characterized by having a very low dielectric constant. In fact, the dielectric constant of a metal is considered to be infinite.

3. **Conductivity of Metals:** Metals are good conductors of electricity due to the presence of free electrons that can move easily through the material. In a metal, the free electrons are not bound to individual atoms and are delocalized, forming what is known as an electron sea. This electron sea allows for the efficient conduction of electric current.

4. **Effect on Electric Field:** When an electric field is applied to a metal, the free electrons in the metal quickly respond to the field and redistribute themselves. As a result, the electric field inside the metal becomes zero. This means that the electric field in a metal is completely shielded by the movement of the free electrons.

5. **No Energy Storage:** Due to the efficient conduction of electric current in metals and the shielding of the electric field, there is no energy storage in the form of electric fields within a metal. Therefore, the dielectric constant of a metal is considered to be infinite.

6. **Practical Implications:** The infinite dielectric constant of metals has practical implications in various fields. For example, in the design and construction of capacitors, metals are often used as the conducting plates since they have a negligible effect on the overall capacitance value.

In conclusion, the dielectric constant of a metal is infinite due to the efficient conduction of electric current and the shielding of the electric field by the movement of free electrons. This property of metals has practical implications in various applications involving capacitors and electric fields.