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Capacitance in a medium

C'=KC

K=C'/ C=110/50=2.2

C' = KC C' = 110pF , C = 50pF 110 = K x 50 K= 110/50 = 2.2  Thus, K = 2.2[no units]  for oil

Bob at pendulum mass 2g, charge , an electric field of intensity 2000v/m. Angle of pendulum with vertical at equilibrium?

• Option 1)

• Option 2)

$\Theta = cot^{-1}{\frac{1}{2}}$

• Option 3)

$\Theta = sin^{-1}{\frac{1}{2}}$

• Option 4)

$\Theta = tan^{-1}{\frac{1}{4}}$

Option 1) Option 2) Option 3) Option 4)

Shown in the figure is a shell made of a conductor. It has inner radius a and outer radius b, and carries charge Q, At its centre is a dipole $\vec{p}$ as shown. In  this case :

• Option 1)

surface charge density on the outer surface depends on $\left|\vec{p} \right |$

• Option 2)

electric field outside the shell is the same as that of a point charge at the centre of the shell

• Option 3)

surface charge density on the inner surface is uniform and equal to $\frac{(Q/2)}{4\pi a^{2}}$

• Option 4)

surface charge density on the inner surface of the shell is zero everywhere

The electric field formed by dipole is non-uniform and hence the charge induced on the inner surface is also non-zero and non-uniform. So far any observed outside the shell, the resultant electric field is due to Q uniformly distributed on outer surface and it is equal to  Option 1) surface charge density on the outer surface depends on  Option 2) electric field outside the shell is the same...

A simple pendulum  of length L is placed between theplates of a parallal plate capacitor having electric field E, as shown in figure. its bob has mass m and charge q. The time period of the pendulum is given by:

• Option 1)

$2\pi \sqrt{\frac{L}{\sqrt{g-\frac{qE}{m}}}}$

• Option 2)

$2\pi \sqrt{\frac{L}{\sqrt{g^{2}-\frac{q^{2}E^{2}}{m^{2}}}}}$

• Option 3)

$2\pi \sqrt{\frac{L}{g+\frac{qE}{m}}}$

• Option 4)

$2\pi \sqrt{\frac{L}{\sqrt{g^{2}+\left ( \frac{qE}{m} \right )^{2}}}}$

Two force act on the mass m 1) gravity force 2) force by electric field. net force on m is = So, net g is = Option 1)  Option 2)  Option 3)Option 4)

In free space , a particle A of charge $1\mu C$ is held fixed at a point P. Another particle B of the same charge and mass of $4\mu g$ is kept at a distance of 1mm from P. If B is relesed .then its velocity at a distance of 9mm from  p is:

$\left [ Take \, \, \frac{1}{4\pi \epsilon _{0}}=9\times 10^{9} Nm^{2}C^{-2}\right ]$

• Option 1)

$1.0m/s$

• Option 2)

$3.0\times 10^{4}m/s$

• Option 3)

$2.0\times 10^{3}m/s$

• Option 4)

$1.5\times 10^{2}m/s$

As we know loss in potential energy =gain in kinetic energy Option 1) Option 2) Option 3) Option 4)

Figure shows charge (q) versus voltage (V) graph for series and parallel combination

of two given capacitors. The capacitances are:

• Option 1)

$40\mu F\: \: and\: \: 10\mu F$

• Option 2)

$60\mu F\: \: and\: \: 40\mu F$

• Option 3)

$50\mu F\: \: and\: \: 30\mu F$

• Option 4)

$20\mu F\: \: and\: \: 30\mu F$

Series Grouping - - wherein     Parallel Grouping - - wherein     For parallel  So,  ............(1) For series So, Option 1) Option 2) Option 3) Option 4)

A point dipole $\vec{p}=-p_{0}\hat{x}$ is kept at the origin. The potential and electric field due to this dipole on the y-axis at a distance d are, respectively : ( Take V=0 at infinity)

• Option 1)

$0,\frac{-\vec{p}}{4\pi\epsilon _{0}d^{3}}$

• Option 2)

$0,\frac{\vec{p}}{4\pi\epsilon _{0}d^{3}}$

• Option 3)

$\frac{\left|\vec{p}\right|}{4\pi\epsilon _{0}d^{2}},\frac{-\vec{p}}{4\pi\epsilon _{0}d^{3}}$

• Option 4)

$\frac{\left|\vec{p}\right|}{4\pi\epsilon _{0}d^{2}},\frac{\vec{p}}{4\pi\epsilon _{0}d^{3}}$

Electric dipole - Two equal and opposite charges seperated by small distance. - wherein                                                                                                                                                                                                                                                Option 1) Option 2) Option 3) Option 4)

Two identical parallel plate capacitors, of capacitance C each, have plates of area A, separated by a distance d. The space between the plates of the two capacitors, is filled with three dieletrics, of equal thickness and dielectric constants $K_{1},K_{2}andK_{3}$. The first capacitors is filled as shown in fig. I, and the second one is filled as shown in fig II.

If these two modified capacitors are charged by the same potential V, the ratio of the energy stored in the two, would be ($\inline E_{1}$ refers to capacitors (I) and $\inline E_{2}$ to capacitor (II) ):

• Option 1)

$\inline \frac{E_{1}}{E_{2}}=\frac{9K_{1}K_{2}K_{3}}{(K_{1}+K_{2}+K_{3})(K_{2}K_{3}+K_{3}K_{1}+K_{1}K_{2})}$

• Option 2)

$\inline \frac{E_{1}}{E_{2}}=\frac{(K_{1}+K_{2}+K_{3})(K_{2}K_{3}+K_{3}K_{1}+K_{1}K_{2})}{9K_{1}K_{2}K_{3}}$

• Option 3)

$\inline \frac{E_{1}}{E_{2}}=\frac{K_{1}K_{2}K_{3}}{(K_{1}+K_{2}+K_{3})(K_{2}K_{3}+K_{3}K_{1}+K_{1}K_{2})}$

• Option 4)

$\inline \frac{E_{1}}{E_{2}}=\frac{(K_{1}+K_{2}+K_{3})(K_{2}K_{3}+K_{3}K_{1}+K_{1}K_{2})}{K_{1}K_{2}K_{3}}$

Arrangement I  capacities in series Arrangement II  capacitors in parallel         Option 1) Option 2) Option 3) Option 4)

A uniformly charged ring of radius 3a and total charge q is placed

in xy-plane centred at origin. A point charge q is moving towards

the ring along the z-axis and has speed v at z=4a. The minimum

value of v such that it crosses the origin is :

• Option 1)

$\sqrt{(\frac{2}{m})}(\frac{4}{15}\frac{q^{2}}{4\pi\varepsilon _oa})^{\frac{1}{2}}$

• Option 2)

$\sqrt{(\frac{2}{m})}(\frac{1}{5}\frac{q^{2}}{4\pi\varepsilon _oa})^{\frac{1}{2}}$

• Option 3)

$\sqrt{(\frac{2}{m})}(\frac{2}{15}\frac{q^{2}}{4\pi\varepsilon _oa})^{\frac{1}{2}}$

• Option 4)

$\sqrt{(\frac{2}{m})}(\frac{1}{15}\frac{q^{2}}{4\pi\varepsilon _oa})^{\frac{1}{2}}$

E and V at a point P that lies on the axis of ring -   ,    -   Potential energy Per unit charge - - wherein S.I unit is .     Use energy conservation Option 1) Option 2) Option 3) Option 4)

The electric filed in a region is given by $\vec{E}=\left ( Ax+B \right )\hat{i}$, where E is in $NC^{-1}$ and x is in meters. The value of constantd are A=20 SI unit and B= 10 SI unit. If the potential at x=1 is V1 and that at x=-1 is V2 , then V1-V2 is:

• Option 1)

320 V

• Option 2)

-48 V

• Option 3)

180 V

• Option 4)

-520 V

Relation between E and V in integral form - -                                                                            Option 1) 320 V Option 2) -48 V Option 3) 180 V Option 4) -520 V

An electric dipole is formes by two equal and opposite charges q with separation d. The charges have same mass m. It is kept in a uniform electric field E. If it is slightly rotated from its equilibrium orientation, then its angular frequency $\omega$ is

• Option 1)

$\sqrt{\frac{qE}{md}}$

• Option 2)

$\sqrt{\frac{2qE}{md}}$

• Option 3)

$2\sqrt{\frac{qE}{md}}$

• Option 4)

$\sqrt{\frac{qE}{2md}}$

Oscillation of dipole - - wherein I - Moment of Inertia of dipole.     Option 1)   Option 2) Option 3) Option 4)

In the given circuit, the charge on $4\mu F$ the capacitor will be:

• Option 1)

5.4 $\mu C$

• Option 2)

9.6 $\mu C$

• Option 3)

13.4 $\mu C$

• Option 4)

24 $\mu C$

Capacitance of Conductor - - wherein C - Capacity or capacitance of conductor  V - Potential.       Option 1) 5.4    Option 2) 9.6  Option 3) 13.4  Option 4) 24

Let a total charge 2 Q be distributed in a sphere of radius R, with the charge density given by $p(r)=kr$, where r is the distance from the centre. Two charge A and B, of -Q each, are placed on diametrically opposite points, at equal distance, a, from the centre. If A and B do not experience any force, then:

• Option 1)

$a=8^{-1/4}R$

• Option 2)

$a=\frac{3R}{2^{1/4}}$

• Option 3)

$a=2^{-1/4}R$

• Option 4)

$a=R/\sqrt{3}$

by Gauss law force  From (1) and (2)   also  from (3) and (4)          Option 1)         Option 2) Option 3) Option 4)

Four point charges $-q,+q \:,\:-q\ and \ +q$ are place on y-axis at  $y=-2d,y=-d,y=+d\:\:and\:\:y=+2d$ respectively . The magnitude of the electric field $E$ at a point on the x-axis at $x=D,$ with $D\gg d$, will behave as :

• Option 1)

$E\propto \frac{1}{D^{3}}$

• Option 2)

$E\propto \frac{1}{D}$

• Option 3)

$E\propto \frac{1}{D^{4}}$

• Option 4)

$E\propto \frac{1}{D^{2}}$

Applying binomial approximation     Option 1)   Option 2) Option 3)   Option 4)

The parallel combination of two air filled parallel plate capacitors of capacitance  C and nC is connected  to a battery of voltage , V . When the capacitors are fully charged , the battery is removed and after that a dielectric material of dielectric constant K is placed between the two plates of the first capacitors . The new potential difference of the combined system is :

• Option 1)

$\frac{nV}{K+n}$

• Option 2)

$V$

• Option 3)

$\frac{V}{K+n}$

• Option 4)

$\frac{(n+1)V}{(K+n)}$

Q should be conserved after removal of battery  Option 1)  Option 2)Option 3)  Option 4)

A parallel plate capacitor has $1\mu F$ capacitance. One of its two plates is given $+2\mu C$ chargre and the other plate, $+4\mu C$ charge. The potential difference developed across the cpacitor is:

• Option 1)

$3 V$

• Option 2)

$1V$

• Option 3)

$5V$

• Option 4)

$2V$

Option 1)Option 2)Option 3)Option 4)

A Positive point charge is released from rest at a distance  ro from a positive line chage with unifrom density. The speed (v) of the point charge , as function of instantaneous distance r from line charge, is proportional to:

• Option 1)

$v \;\alpha \; e^{+r/r_{0}}$

• Option 2)

$v\; \alpha \;\sqrt{\ln \left ( \frac{r}{r_{0}} \right )}$

• Option 3)

$v\; \alpha \;\ln \left ( \frac{r}{r_{0}} \right )$

• Option 4)

$v\; \alpha \; \left ( \frac{r}{r_{0}} \right )$

Apply Energy conservation Option 1) Option 2) Option 3) Option 4)

A solid conducting sphere, having a charge Q, is surrounded by an uncharged conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V. If the shell is now given a charge of $-4\; Q$, the new potential difference between the same two surfaces is :

• Option 1)

$2\; V$

• Option 2)

$V$

• Option 3)

$-2\; V$

• Option 4)

$4\; V$

Initially and After giving to shell Option 1)Option 2)Option 3)  Option 4)

A capacitor with capacitance $5\; \mu F$ is charged to $5\; \mu C$. If the plates are pulled apart to reduce the capacitance to $2\; \mu F,$ how much work is done ?

• Option 1)

$6.25\times 10^{-6}J$

• Option 2)

$3.75\times 10^{-6}J$

• Option 3)

$2.16\times 10^{-6}J$

• Option 4)

$2.55\times 10^{-6}J$

Option 1) Option 2) Option 3)Option 4)

A system of three charges are placed as shown in the figure :

If $D> > d,$ the potential energy of the system is best given by :

• Option 1)

$\frac{1}{4\pi \epsilon _{0}}\left [ -\frac{q^{2}}{d}-\frac{q\; Q\; d}{2D^{2}} \right ]$

• Option 2)

$\frac{1}{4\pi \epsilon _{0}}\left [ -\frac{q^{2}}{d}+\frac{2\; q\; Q\; d}{D^{2}} \right ]$

• Option 3)

$\frac{1}{4\pi \epsilon _{0}}\left [ +\frac{q^{2}}{d}+\frac{q\; Q\; d}{D^{2}} \right ]$

• Option 4)

$\frac{1}{4\pi \epsilon _{0}}\left [ -\frac{q^{2}}{d}-\frac{q\; Q\; d}{D^{2}} \right ]$

Option 1)    Option 2)     Option 3)         Option 4)
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