Partially Filled Dielectrics

Q. The capacitance of a parallel plate capacitor with air as medium is $6\mu \text{F}$. With the introduction of a dielectric medium, the capacitance becomes $30\mu \text{F}$. The permittivity of the medium is: ${\epsilon }_0=8.85\times {10}^{-12}{\text{C}}^2{\text{N}}^{-1}{\text{m}}^{-2}$

1. $0.44\times {10}^{-10}{\text{C}}^2{\text{N}}^{-1}{\text{m}}^{-2}$
2. $5.00{\text{C}}^2{\text{N}}^{-1}{\text{m}}^{-2}$
3. $0.44\times {10}^{-13}{\text{C}}^2{\text{N}}^{-1}{\text{m}}^{-2}$
4. $1.77\times {10}^{-12}{\text{C}}^2{\text{N}}^{-1}{\text{m}}^{-2}$

Q. An electric dipole consisting of two equal and opposite point charges (q, m) and dipole length=2l is slightly disturbed from its position of stable equilibrium. The minimum time during which its gets aligned with the electric field.

Q.

How do capacitors increase DC voltage?

Q. a parallel plate capacitor (without dielectric) is charged by a battery and kept connected to the battery.a dielectric slab of dielectric constant K is inserted between the plates fully occupying the space between the plates.the energy density of electric field between the plates will (1)increase K^2 times (2)decrease K^2 times (3)increase K times (4)decrease K times

Q. For the given charge distribution, net electric field at the centre of non-conducting ring is
(Assume that charge on first quadrant is neutral, second and third quadrant is positively charged, fourth quadrant is negatively charged )

1. $185\text{N/C}$
2. $285\text{N/C}$
3. $384\text{N/C}$
4. $484\text{N/C}$

Q. A thin uniformly charged ring of radius $1\text{m}$, charge $+10\text{C}$ and a semi-infinite charged wire of $\lambda =+10\text{nC/m}$, oriented along the axis of ring with one of its ends coinciding with the centre of the ring, form a system. Find the force of interaction between the ring and wire.

1. $600\text{N}$
2. $700\text{N}$
3. $800\text{N}$
4. $900\text{N}$

Q. Capacitance of a parallel plate capacitor becomes $\frac{4}{3}$ times its original value if a dielectric slab of thickness $t=\frac{d}{2}$ is inserted between the plates [$d$ is the separation between the plates]. The dielectric constant of the slab is

1. $4$
2. $8$
3. $2$
4. $6$

Q. The potential difference between points A and B is

Q. A parallel plate capacitor of capacitance $C$
has spacing d between two plates having area $A$. The region between the plates is filled with N dielectric layers, parallel to its plates, each with thickness $\delta =\frac{d}{N}$. The dielectric constant of the $m^{th}$ layer is $K_m=K(1+\frac{m}{N})$. For a very large $N(>{10}^3)$, the capacitance $C$ is $\alpha \left(\frac{K{\in }_{0}A}{dln2}\right)$. The value of $\alpha$ will be . [${\in }_0$ is the permittivity of free space]

Q. The charge on plate of capacitor varies as q=qosinwt and seperation between plates in very small as compared to area of the plate.The peak value of displacement current through capacitor

Q. A charged wire of length $3\text{m}$ lies along $x-$ axis in such a way that its linear charge density is given by $\lambda =2x^2\text{C/m}$. The total charge on the wire is

1. $15\text{C}$
2. $18\text{C}$
3. $17\text{C}$
4. $16\text{C}$

Q. Consider a parallel-plate capacitor of capacitance $10\mu F$ with air filled in the gap between the plates. Now, one half of the space between the plates is filled with a dielectric of dielectric constant 4 as shown in the figure. The capacitance of the capacitor changes to

1. $25\mu F$
2. $20\mu F$
3. $20\mu F$
4. $40\mu F$

Q. A parallel plate capacitor with plate area $A$ and plate separation $d=2\text{m}$ has a capacitance of $4\mu F$. The new capacitance of the system, if half of the space between them is filled with a dielectric material of dielectric constant $K=3$ (as shown in figure) will be:

Q. In the given circuit, potential difference between points A and B is (i.e $V_{AB})$

1. +20 V
2. -12 V
3. +14 V
4. +8 V

Q. An electric current is passed through a circuit containing two wires of the same material connected in parallel. If the lengths and radii of the wires are in the ratio of $4/3$ and $2/3$ respectively, then the ratio of the currents passing through the wires will be -

1. $1/3$
2. $1/5$
3. $8/9$
4. $2$

Q. Two large non-conducting plates having surface charge densities $+\sigma$ and $-\sigma$ respectively, are fixed $d$ distance apart. A small test charge $q$ of mass $m$ is attached to two non-conducting springs, each of spring constant $k$ as shown in the figure. The sum of lengths of both springs in undeformed state is $d$. The charge $q$ is released from rest with both the spring undeformed. Then charge $q$ will -

$($Neglect gravity$)$

1. Performs SHM with angular frequency $\sqrt{\frac{2k}{m}}$ and amplitude $\frac{\sigma q}{k{ϵ}_0}$.
2. Performs SHM with angular frequency $\sqrt{\frac{2k}{m}}$ and amplitude $\frac{\sigma q}{2k{ϵ}_0}$.
3. Does not perform SHM, but will execute periodic motion.
4. Remains stationary.

Q. A dielectric slab of area $A$ and thickness $d$ is inserted between the plates of a capacitor of area $2A$ with constant speed $v$ as shown in the figure. Distance between the plates is $d$.

The capacitor is connected to a battery of e.m.f. $E$; the current in the circuit varies with time as

1. 
2. 
3. 
4. none of these

Q. A parallel-plate capacitor has a dielectric slab in it. The slab just fills the space inside the capacitor. The capacitor is charged by a battery and then the battery is disconnected. Now, the slab is pulled out slowly at $t=0$. If at time $t$, the capacitance of the capacitor is $C$ and potential difference between the plates of the capacitor is $V$, then which of the following graphs is/are correct.

1. 
2. 
3. 
4. 

Q. An air capacitor of capacity $C=10\mu F$ is connected to a constant voltage battery of $12\text{V}$. Now the space between the plates is filled with a liquid of dielectric constant $5$. The excess charge that flows now from battery to the capacitor is

1. $120\mu C$
2. $600\mu C$
3. $240\mu C$
4. $480\mu C$

Q. Consider the situation shown in figure.


The plates of the capacitor have plate area $A$ and are clamped in the laboratory. The dielectirc slab is released from rest with a length $a$ inside the capacitor. Neglecting any effect of friction or gravity, show that the slab will execute periodic motion and find its time period.

1. $\sqrt{\frac{mld(l-a)}{{\epsilon }_{0}A{E}^{2}A(K-1)}}$
2. $2\sqrt{\frac{mld(l-a)}{{\epsilon }_{0}A{E}^{2}A(K-1)}}$
3. $4\sqrt{\frac{mld(l-a)}{{\epsilon }_{0}A{E}^{2}A(K-1)}}$
4. $8\sqrt{\frac{mld(l-a)}{{\epsilon }_{0}A{E}^{2}A(K-1)}}$

Q. The charge on a capacitor plate in a circuit, as a function of time, is shown in the figure:


What is the value of current at $t=4\text{s}$?

1. $2\mu \text{A}$
2. $1.5\mu \text{A}$
3. $3\mu \text{A}$
4. Zero

Q.

Write a function rule for “the output is half of the input.”

Q. Two long parallel wires $\text{P}$ and $\text{Q}$ placed at a separation of $6\text{cm}$ carries electric currents, $I_1=5\text{A}$ and $I_2=2\text{A}$ respectively in the opposite directions as shown in the figure. Find the point on the line $\text{AB}$ where the resultant magnetic field is zero.

1. $4\text{cm}$ away from $B$ and $10\text{cm}$ away from $A$
2. $4\text{cm}$ away from $B$ and $2\text{cm}$ away from $A$
3. At the midpoint of $AB$
4. None of these

Q. A parallel plate capacitor is made of two square plates of side ${}^{\prime }{a}^{\prime }$, separated by a distance $d(d<<a)$. The lower triangular portion is filled with a dielectric of dielectric constant $K$. The capacitance of this capacitor is :

1. $\frac{1}{2}K\frac{{ϵ}_0{a}^2}{d}$
2. $K\frac{{ϵ}_0{a}^2}{d}\ln K$
3. $K\frac{{ϵ}_0{a}^2}{d(K-1)}\ln K$
4. $K\frac{{ϵ}_0{a}^2}{2d(K+1)}$

Q. A parallel-plate capacitor with no dielectric has a capacitance of $0.5\mu F$. The space between the plates is filled with equal amounts of two dielectric materials of dielectric constants 2 and 3 as shown in the figure. Find the capacitance of the system.

1. $1.2\mu F$
2. $1.8\mu F$
3. $1.25\mu F$
4. None of these

Q. A parallel plate capacitor contains a mica sheet (thickness $={10}^{-3}m$) and a sheet of fibre (thickness $=0.5\times {10}^{-3}m$). The dielectric constant of mica is 8 and that of fibre is 2.5. Assuming that the fibre breaks down when subjected to an electric field of $6.4\times {10}^{6}V/m$, find the maximum safe voltage that can be applied to the capacitor.

1. $2.08kV$
2. $2.08V$
3. $9.6kV$
4. $9.6V$

Q. A parallel plate air capacitor is made using two square plates each of side $0.2\text{m}$, spaced $1\text{cm}$ apart. It is connected to a $50\text{V}$ battery. What is the charge on each plate?

1. $1.77\times {10}^{-3}\text{C}$
2. $1.77\times {10}^{-3}\mu \text{C}$
3. $3.54\times {10}^{-3}\text{C}$
4. $3.54\times {10}^{-3}\mu \text{C}$

Q. a parallel plate capacitor is charged by a I=2*10^-7 . when discharge of the capacitor takes place through a resistance the rate of change of electric flux is??

Q. The capacitor plates are fixed on an inclined plane and connected to a battery of e.m.f. $E$. The capacitor plates have area $A$, length $l$ and the distance between them is $d$. A dielectric slab of mass $m$ and dielectric constant $k$ is inserted into the capacitor and tied to a mass $M$ by a massless string as shown in the figure. Find the value of $M$ for which the slab will stay in equilibrium. There is no friction between slab and plates.

1. $\frac{m}{2}+\frac{E^2{\epsilon }_{0}A(k-1)}{2lgd}$
2. $\frac{m}{2}-\frac{E^2{\epsilon }_{0}A(k-1)}{2lgd}$
3. $\frac{m}{2}-\frac{E^2{\epsilon }_{0}A(k-1)}{lgd}$
4. $\frac{m}{2}+\frac{E^2{\epsilon }_{0}A(k-1)}{2lgd}$

Q.

How much energy can a capacitor store?