Electric Field Due to Disk and Infinitely Large Sheet

Q. ample 1.11 The electric field components in Fig. 1.27 areEr = ax1/2, Ey = Ez = 0, in which α = 800 N/C m1/2. Calculate (a) theflux through the cube, and (b) the charge within the cube. Assumethat a= 0.1 m.

Q.

A parallel plate capacitor is charged and then isolated. The effect of increasing the plate separation, the charge, potential, and capacitance respectively

1. constant, decreases, decreases.

2. increases, decreases, decreases.

3. constant, decreases, increases.

4. constant, increases, decreases.

Q. A large non-conducting sheet $\text{M}$ is given a uniform charge density. Two uncharged small metal rods $\text{A}$ and $\text{B}$ are placed near the sheet as shown in figure. Which of the following options is incorrect?

1. $\text{M}$ attracts $\text{A}$
2. $\text{M}$ attracts $\text{B}$
3. $\text{A}$ attracts $\text{B}$
4. $\text{B}$ repels $\text{A}$

Q. Find the magnitude of the electric field $\left(|\overrightarrow{E_{ind}}|\right)$ at point $\text{A}$ due to the induced charges on the sphere.

1. $\frac{KQ}{5}$
2. $\frac{KQ}{25}$
3. $\frac{KQ}{16}$
4. $\frac{KQ}{4}$

Q. For the given electric field lines configurations, which of the following charge has greater magnitude?

1. $Q_1$
2. $Q_2$
3. $Q_3$
4. $Q_4$

Q.

How does dielectric affect potential difference?

Q. An isolated parallel plate capacitor of capacitance $C$ has four surfaces with charges $Q_1,Q_2,Q_3$ and $Q_4$ as shown in the figure below. The potential difference across plates is (In the given diagram, $Q_1$ and $Q_4$ are the charges on the outer surfaces of the left & right plates respectively)

1. $\frac{[Q_1+Q_2]}{C}$
2. $\left|\frac{Q_2}{C}\right|$
3. $\left|\frac{Q_3}{C}\right|$
4. $\left|\frac{Q_2+Q_3}{C}\right|$

Q. A hydrogen ion and a singly ionized helium atom are accelerated, from rest, through the same potential difference. The ratio of final speeds of hydrogen and helium ions is close to:

1. $1:2$
2. $10:7$
3. $2:1$
4. $5:7$

Q. In a Van de Graaff electrostatic generator a rubber belt of 0.3 m width travels at a velocity of 20m/s. The belt is given a uniform surface charge at lower roller, so it produces a field of ${10}^{6}V/m$ in its vicinity. Current (in milliamperes) carried by the belt is

Q. A straight cylindrical wire of infinite length produces an electric field of strength $9\times {10}^4\text{N/C}$ at a distance of $10\text{cm}$ from wire. The linear charge density of the wire is:

1. $0.1\mu \text{C/m}$
2. $0.5\mu \text{C/m}$
3. $50\mu \text{C/m}$
4. $10\mu \text{C/m}$

Q. Several protons of different speeds enter a uniform magnetic field confined in a cylindrical region. Each proton enters field radially, then choose correct options about time interval spent by them in magnetic field.

1. Faster is particle, lesser is time
2. Faster is particle, greater is time
3. Slower is particle, greater is time
4. Time is independent of speed

Q.

What is K in capacitance?

Q. State Gauss theoram. Derive an experience for the electric field due to charge plane sheet

Q. A spherical cavity of radius $R$ is cut from a non-conducting sphere of volume charge density $\rho {\text{C/m}}^3$ as shown in figure. Find the net electric field at point $\text{P}$. [Take $K=\frac{1}{4\pi {ϵ}_0}$]

1. $\frac{31}{27}K\rho \pi R$, towards right
2. $\frac{35}{27}K\rho \pi R$, towards right
3. $\frac{2}{7}K\rho \pi R$, towards left
4. None of the above

Q.

A square plate of side 2 m contains a charge uniformly distributed over one of its side, such that the surface charge density $\sigma$ is $10C/m^2$. The net charge on the square surface is n coulombs, where n is a natural number. The value of n is __.

Q. State whether given statement is True or False.
Magnitude of electrostatic force due to one point charge on other point charge does not depend on medium in which both of them are placed.

1. True
2. False

Q. Three identical conduting plates $P_1,P_2\text{and}{P}_3$ are kept at a distance $d$ from each other as shown. If $q,-q,2q$ are the charges in $P_1,P_2\text{and}{P}_3$ respectively, the electric field between $P_1\text{and}{P}_2$ is (where $A$ is the area of plate)

1. $\left(\frac{q}{2A{\epsilon }_0}\right)$
2. $\left(\frac{2q}{2A{\epsilon }_0}\right)$
3. 0
4. $\left(\frac{4q}{2A{\epsilon }_0}\right)$

Q. In the figure shown A and B are two charged particles having charges $q$ and $-q$ respectively are placed on a nonconducting fixed horizontal smooth plane. B is fixed and A is attached to a non conducting massless spring of spring constant $K$. The other end of the spring is fixed. Mass of A is $m$, A and B are in equilibrium, when the distance between them is $r$. Choose the correct options

1. time period of small oscillation of block $A$ about is mean position $=2\pi \sqrt{\frac{m}{K-\frac{q^2}{2\pi {ϵ}_0{r}^3}}}$
2. time period of small oscillation of block A about is means position $=2\pi \sqrt{\frac{m}{K+\frac{q^2}{2\pi {ϵ}_0{r}^3}}}$
3. to perform SHM, $K$ must be greater than
   $\frac{q^2}{2\pi {ϵ}_0{r}^3}$
4. Will perform SHM, for any value of $K$

Q. What is the conductivity of a semiconductor (in ${\Omega }^{-1}{\text{m}}^{-1}$) if electron density $5\times {10}^{12}{\text{cm}}^{-3}$ and hole density $8\times {10}^{13}{\text{cm}}^{-3}$
$[{\mu }_e=2.3{\text{m}}^2{\text{V}}^{-1}{\text{s}}^{-1}\text{and}{\mu }_h=0.01{\text{m}}^2{\text{V}}^{-1}{\text{s}}^{-1}]$

1. $5.6$
2. $2.0$
3. $3.4$
4. $8.0$

Q.

The magnitude of electric field due to an infinite uniformly charged insulating sheet is 10 N/C at a point which is at a distance 3m away from it. The surface charge density of the sheet will be?

1. σ = 5ε₀ C/m2

2. σ = 20ε₀ C/m²

3. None of these

4. σ = ε₀ C/m²

Q. Charges q, 2 q, 3 q and 4 q are placed at the corners A, B, C and D of a square as shown in the following figure. The direction of electric field at the center of the square is along.

1. CB
2. AC
3. BD
4. AB

Q.

Given a circular disk of radius R = 0.4 m and containing uniformly distributed charge with surface charge density, $\sigma =1C/m^2$. The electric field at a point P which is 0.3m along the axis of the disc from the centre is $\frac{1}{\eta {\epsilon }_0}$ where n is a natural number whose value is equal to _____

___

Q. For the given spherical Gaussian surface around a point charge $+q$ placed at its centre, angle between electric field $\overrightarrow{E}$ and area vector $\overrightarrow{A}$ at the surface is

1. ${30}^{\circ }$
2. ${60}^{\circ }$
3. ${90}^{\circ }$
4. $0^{\circ }$

Q. One plate of a capacitor is connected to a spring as shown. Area of both the plates is $A$ and separation is $d$ when capacitor is uncharged. When capacitor is charged in steady state separation between the plate is $0.8d$ the force constant of the spring is

1. $\frac{5{\epsilon }_{0}A{E}^2}{2d^3}$
2. $\frac{2{\epsilon }_{0}AE}{d^2}$
3. $\frac{6{\epsilon }_0{E}^2}{A{d}^3}$
4. $\frac{4{\epsilon }_{0}A{E}^2}{d^3}$

Q.
A neutral conducting rod is placed close to infinite charged plane then

1. Rod will be attracted towards plane.
2. Rod will be repulsed from plane
3. Net force on rod will be zero
4. Can't predict

Q. Five equal charges each of value $q$ are placed at the corners of a regular pentagon of side $a$. What will be the electric field at centre $O$, if the charge from one of the corners (say $A$) is removed?

1. $\frac{q}{4\pi {\epsilon }_0{r}^2}$ along $OA$
2. $\frac{2q}{4\pi {\epsilon }_0{r}^2}$ along $OB$
3. $\frac{q^2}{4\pi {\epsilon }_0{r}^2}$ along $OC$
4. $\frac{2q}{4\pi {\epsilon }_0{r}^2}$ along $OA$

Q. Two small spheres each having equal position charge $Q$ (Coulomb) on each are suspended by two insulating strings of equal length $L$ (meter) from a rigid hook (shown in Fig). The whole set up is taken into satellite where there is no gravity. The two balls are now held by electrostatic forces in horizontal position, the tension in each string is:

1. $\frac{Q^2}{16\pi {\epsilon }_o{L}^2}$
2. $\frac{Q^2}{8\pi {\epsilon }_o{L}^2}$
3. $\frac{Q^2}{4\pi {\epsilon }_o{L}^2}$
4. $\frac{Q^2}{2\pi {\epsilon }_o{L}^2}$

Q. Two positively charged particles each of mass $1.7\times {10}^{-27}$ kg and carrying a charge of $1.6\times {10}^{-19}$ C are placed at a distance $r$ apart. If each one experiences a repulsive force equal to its weight, then $r$ is :

1. $1.17m$
2. $1.71m$
3. $0.171m$
4. $0.117m$

Q. A hollow cylinder has a charge q coulomb within it. If $\varphi$ is the electric flux in units of volt meter associated with the curved surface B. the flux linked with the plane surface A in units of volt meter will be

1. $\frac{q}{2{ϵ}_0}$
2. $\frac{q}{{ϵ}_0}-\varphi$
3. $\frac{\varphi }{3}$
4. $\frac{1}{2}(\frac{q}{{ϵ}_0}-\varphi )$

Q. An infinite plane sheet of charge in vacuum has a uniform surface charge density $\sigma$ . The electric field intensity near it is

1. $\frac{\sigma }{{ϵ}_0}$
2. $\frac{\sigma }{2{ϵ}_0}$
3. $\frac{\sigma }{ϵ}$
4. $\frac{\sigma }{2ϵ}$