Question

I have an insulator with dielectric constant k. If I place it in a region in vacuum with a field E, what is the induced field inside the dielectric?

• A. $-\frac{E}{k}$
• B. $E(1-\frac{1}{k})$
• C. $E(1+\frac{1}{k})$
• D. $E(1-k)$

Answer 1

The correct option is B

$E(1-\frac{1}{k})$

In the above question, the external electric field is E and the net field,
$E^{\prime }=\frac{E}{k}$
The difference between the external and the net field must be induced field right?
We have
$E^{\prime }=E-E_{ind}$
$E_{ind}-E-E^{\prime }$
$=E-\frac{E}{k}$
$=E(1-\frac{1}{k})$