Reanalyzing Permittivity

Q. Two charges are at a distance ‘d’ apart. If a copper plate (conducting medium) of thickness $\frac{d}{2}$ is placed between them, the effective force will be

1. $\frac{F}{2}$
2. $\sqrt{2}F$
3. 2F
4. 0

Q. Two equal charges are suspended with non-conducting wires of equal length from the same point. Now, the whole system is taken inside a liquid (water). If the angle between the threads remains same, then calculate the relative permittivity of water. Relative density of both charged particles is $\sigma$.

1. $\frac{1-\sigma }{\sigma }$
2. $\frac{\sigma }{1+\sigma }$
3. $\frac{\sigma }{\sigma -1}$
4. $\frac{1}{\sigma -1}$

Q. Two balls with equal charges are in a vessel with ice at $-{10}^{\circ }\text{C}$ at a distance of $25\text{cm}$ from each other. On forming water at $0^{\circ }\text{C},$ the balls are brought nearer to $5\text{cm}$ for the interaction between them to be the same. If the dielectric constant of water at $0^{\circ }\text{C}$ is $80.$ The dielectric constant of ice at $-{10}^{\circ }\text{C}$ is-

1. $40$
2. $3.2$
3. $20$
4. $6.4$

Q. A force $F$ acts between sodium and chlorine ions of salt (sodium chloride), when ions are $1cm$ apart in air. The permittivity of air and dielectric constant of water are ${\epsilon }_0$ and $K$ respectively. When a piece of salt is placed in water, electrical force acting between sodium and chlorine ions $1cm$ apart is

1. $\frac{F}{K}$
2. $\frac{FK}{{\epsilon }_0}$
3. $\frac{F}{K{\epsilon }_0}$
4. $\frac{F{\epsilon }_0}{K}$

Q. If the shown system is in equilibrium, then the tension in the silk thread is

1. $0.1\text{N}$
2. $0.2\text{N}$
3. $0.3\text{N}$
4. $0.4\text{N}$

Q. A parallel plate capacitor is placed in such a way that its plates are horizontal and the lower plate is dipped into a liquid of dielectric constant $K$ and density $\rho$. Each plate has an area $A$. The plates are now connected to a battery which supplies a positive charge of magnitude $+Q$ to the upper plate. Find the rise in the level of the liquid in the space between the plates.

1. $\frac{(K^2-1)Q^2}{2A^2{K}^2{E}_0\rho g}$
   
2. $\frac{(K^2+1)Q^2}{2A^2{K}^2{E}_0\rho g}$
   
3. $\frac{(K^2-1)Q^2}{A^2{K}^2{E}_0\rho g}$
   
4. $\frac{(K^2+1)Q^2}{A^2{K}^2{E}_0\rho g}$
   

Q. A shell of radius $R$ having uniform surface change density $\sigma {\text{Cm}}^{-2}$ is divided into two parts as shown in the figure. Find the minimum force $F$ required to keep the two parts together.

1. $\frac{1}{4}{\sigma }^2\frac{\pi R^2}{{\epsilon }_0}$
2. $\frac{1}{2}{\sigma }^2\frac{\pi R^2}{{\epsilon }_0}$
3. $\frac{1}{8}{\sigma }^2\frac{\pi R^2}{{\epsilon }_0}$
4. zero

Q. In the given figure, $P_1$ and $P_2$ are the pressure experienced at the points $1$ and $2$ on a charged conductor respectively. Then:

1. $P_1>P_2$
2. $P_1<P_2$
3. $P_1=P_2$
4. can't be interpreted

Q. A force F acts between sodium and chlorine ions of salt (sodium chloride) when put 1 cm apart in air. The permittivity of air and dielectric constant of water are ${\epsilon }_0$ and K respectively. When a piece of salt is put in water electrical force acting between sodium and chlorine ions 1 cm apart is

1. $\frac{F}{K}$
2. $\frac{FK}{{\epsilon }_0}$
3. $\frac{F}{K{\epsilon }_0}$
4. $\frac{F{\epsilon }_0}{K}$

Q. Three large plates A, B and C are placed parallel to each other and charges are given as shown. The charge on left surface of B, if B and C both are earthed is :

1. $6C$
2. $3C$
3. $-3C$
4. $5C$

Q. A force F acts between sodium and chlorine ions of salt (sodium chloride) when put 1 cm apart in air. The permittivity of air and dielectric constant of water are ${\epsilon }_0$ and K respectively. When a piece of salt is put in water electrical force acting between sodium and chlorine ions 1 cm apart is

1. $\frac{FK}{{\epsilon }_0}$
2. $\frac{F}{K{\epsilon }_0}$
3. $\frac{F{\epsilon }_0}{K}$
4. $\frac{F}{K}$

Q. A force F acts between sodium and chlorine ions of salt (sodium chloride) when put 1 cm apart in air. The permittivity of air and dielectric constant of water are ${\epsilon }_0$ and K respectively. When a piece of salt is put in water electrical force acting between sodium and chlorine ions 1 cm apart is

1. $\frac{F}{K}$
2. $\frac{FK}{{\epsilon }_0}$
3. $\frac{F}{K{\epsilon }_0}$
4. $\frac{F{\epsilon }_0}{K}$

Q. Three identical point charges, each of mass m and charge q, hang from three strings as shown in figure and assume the system is in equilibrium. The value of q in terms of m, L, and is:

1. $q=\sqrt{\left(16/5\right)\pi {\epsilon }_{0}mg{L}^{2}si{n}^2\theta tan\theta }$
2. none of these
3. $q=\sqrt{\left(15/16\right)\pi {\epsilon }_{0}mg{L}^{2}si{n}^2\theta tan\theta }$
4. $q=\sqrt{\left(16/25\right)\pi {\epsilon }_{0}mg{L}^{2}si{n}^2\theta tan\theta }$

Q. Select the option which is a characteristic of electrical fields?

1. Electric fields surround charged sources.
2. The direction of the electric field points in the direction a positive test charge would move within the field.
3. Positive test charges would move away from a positive source.
4. Positive test charges would naturally move towards a negative source.
5. All of these are correct.

Q. Two charges are at a distance ‘d’ apart. If a copper plate (conducting medium) of thickness $\frac{d}{2}$ is placed between them, the effective force will be

1. 2F
2. $\frac{F}{2}$
3. \N
4. $\sqrt{2}F$

Q. Four point charges, each of +q, are rigidly fixed at the four corners of a square planar soap film of side ‘a’. The surface tension of the soap film is $\gamma$. The system of charges and planar film are in equilibrium, and $a=k{\left[\frac{q^2}{\gamma }\right]}^{1/N},$ where 'k' is a constant, . Then N is

Q. Column I gives situations involving a charged particle which may be realized under the condition given in column II. Match the situations in column I with the conditions in column II.

Q. Two equal charges are suspended with non-conducting wires of equal length from the same point. Now, the whole system is taken inside a liquid (water). If the angle between the threads remains same, then calculate the relative permittivity of water. Relative density of both charged particles is $\sigma$.

1. $\frac{\sigma }{\sigma -1}$
2. $\frac{\sigma }{1+\sigma }$
3. $\frac{1-\sigma }{\sigma }$
4. $\frac{1}{\sigma -1}$

Q. Conceptual Questions :
Consider two identical conducting spheres whose surfaces are separated by a small distance. One sphere is
given a large net positive charge, and the other is given a small net positive charge. It is found that the force between the spheres is attractive even though they both have net charges of the same sign. Explain how this attraction is possible.

Q. Two identical charged spheres suspended from a common point by two massless strings of length $l$, are initially at a distance $d(d<<l)$ apart because of their mutual repulsion. The charges begins to leak from both the spheres at a constant rate. As a result, the spheres approach each other with a velocity $v$. Then $v$ varies as a function of the distance $x$ between the spheres as

1. $v\propto x^{-\frac{1}{2}}$
2. $v\propto x^{\frac{1}{2}}$
3. $v\propto x^{-1}$
4. $v\propto x$