Question

Voltage applied across a ceramic dielectric produces an electron static field 100 times greater than air what will be the value of dielectric constant

Answer 1

Answer:

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Voltage applied across a ceramic dielectric produces an electrolytic field 100 times greater than air. What will be the value of dielectric constant ?

A. 50

B. 100

C. 150

D. 200

Answer: Option B

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Explanation:

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Answer 2

Given:

Electrostatic field $=100$ times greater than air

To Find:  Value of dielectric constant

Solution:

Consider a parallel plate capacitor having a ceramic dielectric with a dielectric constant $\[\kappa \]$ inserted between the plates.

The potential difference changes because of the induced charges on the edges of the dielectric as shown in the figure.

Now, the electric field inside the capacitor is given as:

$\[E = \frac{{\sigma - {\sigma _p}}}{{{\varepsilon _o}}}\]$

The potential difference across the capacitor is given as:

$\[\begin{gathered} V = Ed \hfill \\ V = \frac{{\sigma - {\sigma _p}}}{{{\varepsilon _o}}}d \hfill \\ \end{gathered} \]$

If the total electric field with dielectric is $E$ and the total electric field without dielectric is $\[{E_o}\]$, the ratio of both of these electric fields is given as:

$\[\frac{E}{{{E_o}}} = \frac{{\sigma - {\sigma _p}}}{\sigma } = \frac{1}{\[\kappa \]}\]$

Thus, the dielectric constant is the ratio of the electric field with a dielectric to the electric field without a dielectric, i.e.,

$\[\kappa = \frac{{{E_o}}}{E}\]$

As the electric field with dielectric is 100 times greater than air, therefore, $\[E = 100\,{E_o}\]$

Thus,

$\[\begin{gathered} \kappa = \frac{{{E_o}}}{{100\,{E_o}}} \hfill \\ \kappa = \frac{1}{{100}} \hfill \\ \end{gathered} \]$

Hence, the value of the dielectric constant is $\[\frac{1}{{100}}\]$.

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