Two Infinite Sheets

Q. Three identical metal plates with large surface areas are kept parallel to each other as shown in figure. The leftmost plate is given a charge $Q$, the rightmost, a charge $-2Q$ and the middle one remains neutral. Find the charge appearing on the outer surface of the rightmost plate.

1. $\frac{Q}{2}$
2. $\frac{Q}{4}$
3. $-\frac{Q}{2}$
4. $-\frac{Q}{4}$

Q. Two concentric spherical shells of radii $R$ and $r$ have similar charges with equal surface charge densities $\left(\sigma \right)$.
What is the electric potential at their common centre ?

1. $\sigma R/{ϵ}_0$
2. $\frac{\sigma }{{ϵ}_0}(R-r)$
3. $\frac{\sigma }{{ϵ}_0}(R+r)$
4. None of these

Q. The current density at a point is $\overrightarrow{J}=(2\times {10}^4\hat{j}){\text{Am}}^{-2}$. Find the rate of charge flow through a cross-sectional area $\overrightarrow{S}=(2\hat{i}+3\hat{j}){\text{cm}}^2$.

1. $6$
2. $7$
3. $15$
4. $20$

Q. The electric field at a distance ${}^{\prime }{r}^{\prime }$ from an infinitely long conducting sheet is proportional to

​​​​​​​$[$1 Mark$]$

1. $r^{-1}$
2. $r^2$
3. $r^{-\frac{3}{2}}$
4. independent of $r$

Q. Two parallel plane sheets 1 and 2 carry uniform charge densities ${\sigma }_1$ and ${\sigma }_2$ as in fig electric field in the region marked II is (${\sigma }_1$ > ${\sigma }_2$)

1. $-\frac{({\sigma }_1+{\sigma }_2)}{2{ϵ}_0}$
2. $\frac{-\left({\sigma }_1{\sigma }_2\right)}{2{ϵ}_0}$
3. $\frac{({\sigma }_1+{\sigma }_2)}{2{ϵ}_0}$
4. $\frac{({\sigma }_1-{\sigma }_2)}{2{ϵ}_0}$

Q. Find the electric field at point $\text{P}$ as shown in figure due to an infinite long uniformly charged non-conducting thick sheet.

1. $10\text{N/C}$
2. $20\text{N/C}$
3. $30\text{N/C}$
4. $40\text{N/C}$

Q. In the given figure, ${\sigma }_1$ and ${\sigma }_2$ are the surface charge densities around points $1$ and $2$ respectively. Then the relation between the electric fields $E_1$ and $E_2$ near the points $1$ and $2$ respectively will be :

1. $E_1>E_2$
2. $E_1<E_2$
3. $E_1=E_2$
4. can't be interpreted

Q. Two infinite plane parallel sheets, separated by a distance d have equal and opposite uniform charge densities s. Electric field at a point between the sheets is:

1. $\frac{\sigma }{2{ϵ}_0}$
2. $\frac{\sigma }{{ϵ}_0}$
3. Depends on the location of the point
4. Zero

Q. Four large identical metal plates are placed as shown in the figure. Plate $2$ is given a charge $Q$. All other plates are neutral. Now Plate $1$ and $4$ are earthed. Area of each plates is $A$. The charge appearing on the right side of plate $3$ is

1. $Q$
2. $\frac{Q}{2}$
3. $\frac{Q}{8}$
4. $\frac{Q}{4}$

Q. Find the electric field at point $\text{P}$ as shown in figure due to an infinite long uniformly charged non-conducting thick sheet.

1. $10\text{N/C}$
2. $20\text{N/C}$
3. $30\text{N/C}$
4. $40\text{N/C}$

Q. Three large parallel plates have uniform surface charge densities as shown in the figure. The electric field intensity at point P is :

1. $-\frac{4\sigma }{{ϵ}_0}\hat{k}$
2. $\frac{-3\sigma }{2{\epsilon }_0}\hat{k}$
3. $\frac{5\sigma }{2{\epsilon }_0}\hat{k}$
4. $-\frac{5\sigma }{2{\epsilon }_0}\hat{k}$

Q.

The infinite sheets of uniform charge density $10\frac{\mu C}{m^2},-10\frac{\mu C}{m^2}and5\frac{\mu C}{m^2}$ are placed in vacuum as shown. The direction of field intensity at points A and B are respectively?

1. Right, left

2. Left, Right

3. Right, Right

4. Left, Left

Q. Two tiny spheres carrying charges $1.5\mu C$ and $2.5\mu C$ are located 30 cm apart. Find the potential and electric field:

Q. Four large identical metal plates are placed as shown in the figure. Plate $2$ is given a charge $Q$. All other plates are neutral. Now Plate $1$ and $4$ are earthed. Area of each plates is $A$. The charge appearing on the right side of plate $3$ is

1. $\frac{Q}{4}$
2. $\frac{Q}{2}$
3. $Q$
4. $\frac{Q}{8}$

Q. Let $U_a$ and $U_d$ be the energy densities in air and in a dielectric of constant k for same field. Then,

1. $U_a=U_d$
2. $U_a=k{U}_d$
3. $U_d=k{U}_a$
4. $U_a=(k-1)U_d$

Q.

A uniformly charged spherical conductor has a radius of 1m and surface charge density $0.8\frac{C}{m^2}$. The electric field magnitude because of this at a point 1m radially away, from the surface of the sphere is

1. $4.5\times {10}^9\frac{N}{C}$

2. $9\times {10}^9\frac{N}{C}$

3. $2.25\times {10}^{10}\frac{N}{C}$

4. $7.2\times {10}^9\frac{N}{C}$

Q.

The potential difference between two parallel plates is ${10}^4$ volt. If the plates are separated by $0.5cm$, the force on an electron between the plates is :

1. $2\times {10}^{4}N$
2. $3.2\times {10}^{-13}N$
3. $32\times {10}^{12}N$
4. $20N$

Q. Two parallel plane sheets 1 and 2 carry uniform charge densities ${\sigma }_1$ and ${\sigma }_2$ as in fig electric field in the region marked II is (${\sigma }_1$ > ${\sigma }_2$)

1. $-\frac{({\sigma }_1+{\sigma }_2)}{2{ϵ}_0}$
2. $\frac{-\left({\sigma }_1{\sigma }_2\right)}{2{ϵ}_0}$
3. $\frac{({\sigma }_1+{\sigma }_2)}{2{ϵ}_0}$
4. $\frac{({\sigma }_1-{\sigma }_2)}{2{ϵ}_0}$

Q. Two parallel conducting plates of area A = 2.5 $m^2$ each are placed 6 mm apart and are both earthed. A third plate, identical with the first two, is placed at a distance of 2 mm from one of the earthed plates and is given a charge of 1 C. The potential of the central plate is

1. $6\times {10}^{7}V$
2. $3\times {10}^{7}V$
3. $4\times {10}^{7}V$
4. $2\times {10}^{7}V$

Q. If the electric field to the right of the two sheets is $K\sigma /{\epsilon }_0$. Find K?

Q. Charges $2q$ and $-3q$ are given to two identical metal plates of cross-sectional area $A$. The distance between the plates is $d$. The capacitance of system and potential difference between plates respectively will be:

1. $\frac{A{ϵ}_0}{2d},\frac{2.5qd}{{ϵ}_{0}A}$
2. $\frac{2A{ϵ}_0}{d},\frac{qd}{2{ϵ}_{0}A}$
3. $\frac{A{ϵ}_0}{d},\frac{2.5qd}{{ϵ}_{0}A}$
4. $\frac{A{ϵ}_0}{d},\frac{5qd}{{ϵ}_{0}A}$

Q. Two infinite parallel metal planes, contain electric charges with charge densities $+\sigma$ and $-\sigma$ respectively and they are separated by a small distance in air. If the permittivity of air is ${ϵ}_0$, then the magnitude of the field between the two planes with its direction will be:

1. $\sigma /{ϵ}_0$ towards the positively charge plane
2. $\sigma /{ϵ}_0$ towards the negatively charged plane
3. $\sigma /\left(2{ϵ}_0\right)$ towards the positively charged plane
4. $0$ and towards any direction

Q.

Two large conducting plates are placed parallel to each other with a separation of 2.00 cm between them. An electron starting from rest near one of the plates reaches the other plate in 2.00 microseconds. Find the surface charge density on the inner surfaces.

Q.

There identical metal plates with large surface areas are kept parallel to each other as shown in figure (30-E8). The leftmost plate is given a charge Q.the rightmost a charge -2Q and the middle one remains neutral. Find the charge appearing on the outer surface of the rightmost plate.

Q. Two parallel plane sheets 1 and 2 carry uniform charge densities ${\sigma }_1$ and ${\sigma }_2$ as in fig electric field in the region marked II is (${\sigma }_1$ > ${\sigma }_2$)

1. $-\frac{({\sigma }_1+{\sigma }_2)}{2{ϵ}_0}$
2. $\frac{-\left({\sigma }_1{\sigma }_2\right)}{2{ϵ}_0}$
3. $\frac{({\sigma }_1+{\sigma }_2)}{2{ϵ}_0}$
4. $\frac{({\sigma }_1-{\sigma }_2)}{2{ϵ}_0}$

Q.

The electric field E is measured at a point P(0, 0, d) generated due to various charge distributions and the dependence of E on d is found to be different for different charge distributions. List - I contains different relations between E and d. List - II describes different electric charge distributions, along with their locations. Match the functions in List - I with the related charge distributions in List - II

List - I	List - II
(P) E is independent of d	(1) A point charge Q at the origin
(Q) $E\propto \frac{1}{d}$	(2) A small dipole with point charges Q at $(0,0,l)$ and - Q at $(0,0,-l)$. Take $2l<<d$
(R) $E\propto \frac{1}{d^2}$	(3) A infinite line charge coincident with the x-axis, with uniform linear charge density $\lambda$.
(S) $E\propto \frac{1}{d^3}$	(4) Two infinite wires carrying uniform linear charge density parallel to the x-axis. The one along ($y=0,z=l$) has a charge density + $\lambda$ and the one along $(y=0,z=-l)$ has a charge density $-\lambda$. Take $2l<<d$
	(5) Infinite plane charge coincident with the xy-plane with uniform surface charge density

1. $P\to 5;Q\to 3,4;R\to 1;S\to 2$
2. $P\to 5;Q\to 3;R\to 1,4;S\to 2$
3. $P\to 5;Q\to 3;R\to 1,2;S\to 4$
4. $P\to 4;Q\to 2,3;R\to 1;S\to 5$

Q.

The infinite sheets of uniform charge density $10\frac{\mu C}{m^2},-10\frac{\mu C}{m^2}and5\frac{\mu C}{m^2}$ are placed in vacuum as shown. The direction of field intensity at points A and B are respectively?

1. Left, Left

2. Left, Right

3. Right, left

4. Right, Right