Question

The dielectric constant of a metal is:
A. Zero
B. Infinite
C. 1
D. 10

Answer 1

Hint: The ratio of applied electric field to the reduced electric field gives us the dielectric constant. For a metal there is no electric field inside a metal conductor since the free charges reside on the surface of metal only therefore the lower term in the ratio becomes zero.

Complete step by step answer:
Dielectric constant of a material is dependent on the nature of the material. The ratio of external electric field \[{{E}_{0}}\] applied to the reduced value of electric field \[E\], and is constant for a material denoted by K and is called dielectric constant of the material. Here, \[{{E}_{0}}\] is the electric field in the absence of the dielectric material and \[E\] is the electric field in the presence of dielectric material.
\[K=\dfrac{{{E}_{0}}}{E}\]
In case of a metal conductor the free charge carriers reside on the metal surface and net charge inside the conductor is zero and hence the net electric field inside the conductor is also zero.
Since
\[E=0\]
Therefore,
\[K=\infty \]
Thus, the correct option is B. Infinite.

Additional Information:
If we place a dielectric material in an external electric field its polarization occurs. If we go on increasing the field strength a point will come when the dielectric material becomes conducting. This is called electric breakdown. The maximum electric field a material can withstand without breaking down of its insulating property is called its dielectric strength.

Note: The same formula can also be written as:
\[K=\dfrac{\varepsilon }{{{\varepsilon }_{0}}}\] , here \[\varepsilon \]is the permittivity of metal and \[{{\varepsilon }_{0}}\]is the permittivity of free space .Permittivity is ability of a material to resist the formation of electric field inside it and for metals electric field does not exist inside the conductor. Therefore, permittivity of metal is infinitely larger than the permittivity of free space hence the dielectric constant is infinite.