Electric Field

Q. A hollow cylindrical box of length 1 m and area of cross section 25 cm^2 is placed in a three-dimensional coordinate system as shown in the figure. The electric field in the region is given by E=50x \overset{}{i, where E is in N/C and x in metre.} Find (1) net flux through the cylinder (2) charge enclosed by the cylinder.

Q. Consider the charges q , q , -q placed at the vertices of an equilateral triangle . What is the force on each charge ?

Q. A toy car with charge $q$ moves on a frictionless horizontal plane surface under the influence of a uniform electric field $\overrightarrow{E}$. Due to the force $q$$\overrightarrow{E}$, its velocity increases from $0m/s$ to $6m/s$ in one second. At that instant the direction of the field is reversed. The car continues to move for two more seconds under the influence of this field. The average velocity and the average speed of the toy car between $0$ to $3$ seconds are respectively

1. $2m/s,4m/s$
2. $1m/s,3m/s$
3. $1m/s,3.5m/s$
4. $1.5m/s,3m/s$

Q. A point charge $q_1$ exerts an electric force on a second point charge $q_2$. If a third charge $q_3$ is brought near to $q_2$, the electrostatic force exerted by $q_1$ on $q_2$ will
(Presence of charges in the vicinity does not change the force between any two charges)

1. decrease
2. increase
3. remain unchanged
4. increases, if $q_3$ is of same sign as $q_1$ and decreases, if $q_3$ is of opposite sign.

Q.

A charge Q is divided into two parts of q and Q-q . if the coulomb
Repulsion between them when they are separated is to be maximum, the ratio of Q/q should be...

Q.

A block of mass m containing a net positive charge q is placed ona smooth horizontal table which terminates in a vertical wall as shown in figure (29-E2).The distance of the block from the wall is d. A horizontal electric field E towards right is switched on. Assuming elastic collisions (if any) find he time period of the resulting oscillatory motion. Is it a simple sharmonic motion?

Q. A cube with each side a is kept in an electric field given by E=Cx i as shown in the figure, where C is a positive dimensional cons†an t. Find out (1) the electric flux through the cube (2) the net charge inside the cube

Q.

An oil drop of 12 excess electrons is held stationary under a constant electric field of 2.55 × 10⁴ N C⁻¹ in Millikan’s oil drop experiment. The density of the oil is 1.26 g cm⁻³. Estimate the radius of the drop. (g = 9.81 m s⁻²; e = 1.60 × 10⁻¹⁹ C).

Q. two point charges Q and 4Q are 12 cm apart. Sketch the lines of force and calculate the distance of neutral point from 4Q charge

Q. Two identical tennis balls each having mass ${}^{\prime }{m}^{\prime }$ and charge ${}^{\prime }{q}^{\prime }$ are suspended from a fixed point by threads of length ${}^{\prime }{l}^{\prime }$. What is the equilibrium separation when each thread makes a small angle $\theta$ with the vertical ?

1. $x={\left(\frac{q^{2}l}{2\pi {\epsilon }_{0}mg}\right)}^{\frac{1}{2}}$
2. $x={\left(\frac{q^2{l}^2}{2\pi {\epsilon }_0{m}^{2}g}\right)}^{\frac{1}{3}}$
3. $x={\left(\frac{q^{2}l}{2\pi {\epsilon }_{0}mg}\right)}^{\frac{1}{3}}$
4. $x={\left(\frac{q^2{l}^2}{2\pi {\epsilon }_0{m}^2{g}^2}\right)}^{\frac{1}{3}}$

Q. In a neutral sphere , 5×10^{21 }electrons are present. If ten percent electrons are removed, then calculate the charge on the sphere? Calculate the number of electrons in 100 grams of CO2

Q. Two infinite planes each with uniform surface charge density $+\sigma C/m^2$ are kept in such a way that the angle between them is ${30}^o$. The electric field in the region shown between them is given by:

1. $\frac{\sigma }{2{ϵ}_0}\left[\right(1-\frac{\sqrt{3}}{2})\hat{y}-\frac{1}{2}\hat{x}]$
2. $\frac{\sigma }{2{ϵ}_0}\left[\right(1+\frac{\sqrt{3}}{2})\hat{y}-\frac{1}{2}\hat{x}]$
3. $\frac{\sigma }{2{ϵ}_0}\left[\right(1-\frac{\sqrt{3}}{2})\hat{y}+\frac{1}{2}\hat{x}]$
4. $\frac{\sigma }{2{ϵ}_0}\left[\right(1+\frac{\sqrt{3}}{2})\hat{y}+\frac{1}{2}\hat{x}]$

Q. An electron falls from rest through a vertical distance $h$ in a uniform and vertically upward directed electric field $E$. The direction of electric field is now reversed, keeping its magnitude the same. A proton is allowed to fall from rest in it through the same vertical distance $h$. The time of fall of the electron as compared to the time of fall of the proton is

1. $10$ times greater
2. smaller
3. equal
4. $5$ times greater

Q. consider the charges q q and -q placed at the vertices of an equilateral triangle, as shown. What is the force on each charge?this is the example sum 1.7 from ncert textbook

Q. Five point charges, each of value $+q$ are placed on five vertices of a regular hexagon of side $L$. The magnitude of the force on a point charge of value $-q$ placed at the centre of the hexagon is $\frac{n{q}^2}{4\pi {ϵ}_0{L}^2}$. Then the value of n?

Q.

The electric field in a region is given by
$E=(2\hat{i}+3\hat{j})\times {10}^{3}N{C}^{-1}$
The electric flux through a rectangular surface $10cm\times 20cm$ held parallel to the y-z plance is

1. $50N{C}^{-1}{m}^2$

2. $40N{C}^{-1}{m}^2$

3. $60N{C}^{-1}{m}^2$

4. zero

Q.

What is a uniform electric field?

Q. Three charges of equal magnitude q are placed at the vertices of an equilateral triangle of side l. Find net force on any one charge ?

Q. A point charge of +6 μ C coulomb is placed at a distance 20cm directly above the center of a square of side 40cm. The magnitude of the flux through the square is

Q.

Equal charges each of 20 micro column are placed at x=0, 2, 4, 8, 16 cm on x-axis . find the force experienced by the charge at x=2 cm

Q. calulate the field due to an electric dipole of length 10cm and consisting of charge of \pm100micro coulomb at apoint 20 cm from each charge .

Q. An electric field of magnitude ${10}^5\text{N/C}$ points due west at certain point. The magnitude of the force that acts on a charge of $+2\mu C$ and $-5\mu C$ at this point respectively are

1. $0.5\text{N}$ and $0.2\text{N}$
2. $0.2\text{N}$ and $0.5\text{N}$
3. $1\text{N}$ and $0.3\text{N}$
4. $2\text{N}$ and $0.1\text{N}$

Q. Two charges $\sqrt{3}C$ and q C are placed at (2, 0) and (0.2). The direction of intensity of electric field at (2, 2) makes an angle ${30}^{\circ }$ with y–axis then q is:

1. 1C
2. 2C
3. 3C
4. $\sqrt{3}C$

Q. 70.ABC is an equilateral triangle of side 10 m and D is the mid point of BC charges of +100, -100and+75uC are placed at B, C, D respectively.Find the force on a+1uC charge placed at A.

Q. A particle of mass ${10}^{-3}$ kg and charge 1.0 C, is initially at rest. At time $t=0$, the particle comes under the influence an electric field $E\left(t\right)=E_{0}sin\left(\omega t\right)\hat{i}$ where $E_0=1.0N/C$ and $\omega ={10}^3$ $rad/s$ . Consider the effect of only the electrical force on the particle. Then the maximum speed, in $m/s$ , attained by the particle at subsequent times is

Q. A charge Q is placed at the centre of the line joining two equal charges q. Show that the system of three charges will be in equilibrium if $Q=\frac{-q}{4}$.

Q.

Three infinite long plane sheets carrying uniform charge densities
${\sigma }_1=-\sigma ,{\sigma }_2=+2\sigma$ and ${\sigma }_3=+3\sigma$ are placed parallel to the x-z plane at y =a, y=3a and y=4a as shown in Fig. 20.18. The electric field at point P is

1. zero

2. $-\frac{3\sigma }{{ϵ}_0}\hat{j}$

3. $\frac{3\sigma }{{ϵ}_0}\hat{j}$

4. $-\frac{2\sigma }{{ϵ}_0}\hat{j}$

Q. There is a uniform electric field of strength ${10}^{3}V/m$ along y-axis. A body of mass 1g and charge ${10}^{-6}C$ is projected into the field from origin along the positive x-axis with a velocity 10 m/s. Its speed in m/s after 10s is (Neglect gravitation)

1. 10
2. 20
3. $5\sqrt{2}$
4. $10\sqrt{2}$

Q. (a) Two point charges $+Q_1$ and $–Q_2$ are placed $r$ distance apart. Obtain the expression for the amount of work done to place a third charge $Q_3$ at the midpoint of the line joining the two charges.

(b) At what distance from charge $+Q_1$ on the line joining the two charges (in terms of $Q_1,Q_2$ and $r$) will this work be done be zero.

Q. Two concentric conducting thin shells of radius R and 2R carry charges +Q, +3Q respectively. Themagnitude of electric field at a distance x outside (P) and inside (Q) from the surface of outer sphere is same. Then the value of x is