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MODEL PAPER 3 — Physics STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 SciencePhysicsMODEL PAPER 35 Marks
Question
$i. A$ Why does the electric field inside a dielectric slab decrease when kept in an external electric field?
$B$. Derive an expression for the capacitance of a parallel plate capacitor filled with a medium of dielectric constant K.
$ii$. A charge $q =2 \mu C$ is placed at the centre of a sphere of radius $20 \ cm$ . What is the amount of work done in moving $4 \mu C$ from one point to another point on its surface?
$iii.$ Write a relation for polarisation $\overrightarrow{ P }$ of a dielectric material in the presence of an external electric field.
✓

Answer

$i. A. A$ dielectric material gets polarized when it is placed in an external electric field.
The field produced due to the polarization of material reduces the effect of external electric field.
Hence, the electric field inside a dielectric decreases.
$B$. Electric field in vacuum between the plates $= E 0=\frac{\sigma}{\varepsilon_0}$
Electric field in dielectric between the plates, $E =\frac{E_0}{K}$
Potential difference between the capacitor plates
$V=E t+E_0(d-t)$
where $'t\ '$ is the thickness of dielectric slab.
$ V =\frac{E_0}{K} t + E _0(d- t )$
$V =\frac{\sigma}{\varepsilon_o}\left[\frac{t}{K}+( d - t )\right]$
$V =\frac{\sigma}{\varepsilon_o}\left[\frac{t+K(d-t)}{K}\right]$
$\text { As } C =\frac{Q}{V}$
$\Rightarrow C =\frac{\varepsilon_0 A K}{t+K(d-t)}$
$ii.$ The surface of the sphere is equipotential.
So, the work done in moving the charge from one point to the other is zero.
$ W = q \Delta V (\because \Delta V =0)$
$=0$
$iii. P =\chi E$

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