Question: Q. 3. (i) Explain, using suitable diagrams, the difference in the behaviour of (a) conductor and (b) dielectric in the presence of an external electric field. Define the terms polarization of a dielectric and write its relation with susceptibility.

(ii) A thin metallic spherical shell of radius $R$ carries a charge $Q$ on its surface. A point charge $\frac{\mathscr{Q}}{2}$ is placed at its centre $C$ and another charge $+2 Q$ is placed outside the shell at a distance $x$ from the centre as shown in the figure. Find (a) the force on the charge at the centre of shell and at the point $A$, (b) the electric flux through the shell.

U] [Delhi I, II, III 2015]

(a) In the presence of electric field, the free charge carriers, in a conductor, move the charge distribution in the conductor re-adjusting itself so that the net electric field within the conductor becomes zero.

$$ 1 / 2 $$

(b) In a dielectric, the external electric field induces a net dipole moment, by stretching/reorienting the molecules. The electric field, due to this induced dipole moment, opposes, but does not exactly cancel, the external electric field.

$1 / 2$ Polarisation : Induced dipole moment, per unit volume, is called the polarization. For linear isotropic dielectrics having a susceptibility $\chi_{C}$, we have

$$ \begin{equation*} P=\chi_{C} E \tag{1} \end{equation*} $$

(ii) (a) Net Force on the charge $\frac{Q}{2}$, placed at the centre of the shell, is zero.

1 Force oncharge $2 Q$ kept at point $A$

$$ F=E \times 2 Q $$

$$ \begin{aligned} & =\frac{1\left(\frac{3 Q}{2}\right) 2 Q}{4 \pi \varepsilon_{0} x^{2}} \ & =\frac{6 Q^{2}}{8 \pi \varepsilon_{0} x^{2}}=\frac{3 Q^{2}}{4 \pi \varepsilon_{0} x^{2}} \end{aligned} $$

OR

$$ \frac{(k) 3 Q^{2}}{x^{2}} $$

where, $k=\frac{1}{4 \pi \varepsilon_{0}}$

(b) Electric flux through the shell

$$ \phi=\frac{Q}{2 \varepsilon_{0}} $$

$\because$ Charge enclose is $\frac{Q}{2}$

[CBSE Marking Scheme 2015]

AT Q. 4. (i) Compare the individual dipole moment and the specimen dipole moment for $\mathrm{H}{2} \mathrm{O}$ molecule and $\mathrm{O}{2}$ molecule when placed in

(a) Absence of external electric field.

(b) Presence of external electric field.

Justify your answer.

(ii) Given two parallel conducting plates of area $A$ and charge densities $+\sigma$ and $-\sigma$. A dielectric slab of constant $\kappa$ and a conducting slab of thickness $d$ each are inserted in between them as shown.

(a) Find the potential difference between the plates.

(b) Plot $E$ versus $x$ graph, taking $x=0$ at positive plate and $x=5 d$ at negative plate.

U[CBSE SQP 2015-16]

Show Answer

Solution:

Ans. (i)

Non-polar $\left(\mathbf{O}_{2}\right)$ Polar $\left.\mathbf{( H}_{\mathbf{2}} \mathbf{O}\right)$
In absence of
electric field
No dipole
moment exists.
Dipole moment
exists.
Individual No dipole
moment exists.
Dipoles
randomly
oriented. Net $\mathrm{P}=0$
In presence of
electric field
Dipole moment
exists (molecules
become
polarised.)
Torque acts on the
molecules to align
them parallel to E.
Individual dipole
Specimen Dipole moment
exists.
Net
moment
parallel to E.

(ii) (a) $\quad V=E_{0} d+\frac{E_{0}}{\kappa} d+E_{0} d+0+E_{0} d$



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