Infinite Sheet

Q.

The maximum electric field strength E due to a uniformly charged ring of radius r, happens at a distance x, where value of x is (x is measured from the centre of the ring)

1. x = R

2. $x=\frac{R}{2}$

3. $x=\frac{R}{\sqrt{2}}$

4. $x=\sqrt{2}R$

Q. An electron falls through a distance of 1.5 cm in a uniform electric field of magnitude 2x10^{4 N/C} .What is the time of fall.

Q. A body having specific charge \(8 ~\mu\text{C/g}\) is resting on a frictionless plane at a distance \(10~\text{cm}\) from the wall (as shown in the figure). It starts moving towards the wall when a uniform electric field of \(100~\text{V/m}\) is applied horizontally towards the wall. If the collision of the body with the wall is perfectly elastic, then the time period of the motion, in second will be ______.



Body 100 V/m 

Q. In a region of space, the electric field is given by $\overrightarrow{E}=8\hat{i}+4\hat{j}+3\hat{k}$. The electric flux through a surface of area of $100\text{units}$ in $x-y$ plane is

1. $800\text{units}$
2. $300\text{units}$
3. $400\text{units}$
4. $1500\text{units}$

Q. (a) Define electric dipole moment. Is it a scalar or a vector ? Derive the expression for the electric field of a dipole at a point on the equatorial plane of the dipole.
(b) Draw the equipotential surfaces due to an electric dipole. Locate the points where the potential due to the dipole is zero.

Q.

If the dot product of two non-zero vectors is zero, then the vectors

1. can have any orientation.
2. are anti-parallel to each other.
3. are parallel to each other.
4. are perpendicular to each other.

Q.

A charged ball B hangs from a silk thread S, which makes an angle $\theta$ with a large charged conducting sheet P, as shown in the figure. The surface charge density $\sigma$ of the sheet is proportional to

1. $sin\theta$
2. $tan\theta$
3. $cos\theta$
4. $cot\theta$

Q. (a) Define electric flux. Write its S.I. unit. "Gauss's law in electrostatics is true for any closed surface, no matter what its shape or size is". Justify this statement with the help of a suitable example.
(b) Use Gauss's law to prove that electric field inside a uniformly charged spherical shell is zero.

Q. Figure shows four solid spheres, each with charge Q uniformly distributed through its volume. The figure also shows a point P for each sphere, all at the same distance from the center of the sphere. Rank the spheres according to the magnitude of the electric field they produce at point P.

1. $III\to II\to I\to IV$
2. All tie
3. $II\to I\to III\to IV$
4. $I\text{\&}II\text{tie}\to III\to IV$

Q. Let $E_1\left(r\right),E_2\left(r\right)$ and $E_3\left(r\right)$ be the respective electric fields at a distance $r$ from a point charge $Q$, an infinitely long wire with constant linear charge density $\lambda$, an infinite plane with uniform surface charge density $\sigma$.
If $E_1\left(r_0\right)=E_2\left(r_0\right)=E_3\left(r_0\right)$ at a given distance $r_0$, then

1. $Q=4\sigma \pi r_0^2$
2. $r_0=\frac{\lambda }{2\pi \sigma }$
3. $Q=2\sigma \pi r_0^2$
4. $r_0=\frac{\lambda }{\pi \sigma }$

Q. Two charges of magnitude 10 units and 20 units are separated by a certain distance. Now, both the charges are brought in contact and again separated to initial separation. What will be the ratio of initial and final electrostatic force?

1. $\frac{9}{8}$
2. $\frac{4}{3}$
3. $\frac{3}{2}$
4. $\frac{8}{9}$

Q. Which of the following curves between electric field $\left(E\right)$ at a distance $\left(x\right)$ from an infinite long uniformly charged sheet is correct?
[Assume $x$ to be very small as compared to dimension of sheet]

1. 
2. 
3. 
4. 

Q.

A charge $Q$ is distributed over three concentric spherical shells of radii $a,b,c\left(a<b<c\right)$ such that their surface charge densities are equal to one another. The total potential at a point at distance $r$ from their common centre, where $r<a$, would be :

1. $\frac{Q}{4{\mathrm{\pi \epsilon }}_0\left(\mathrm{a}+\mathrm{b}+\mathrm{c}\right)}$

2. $\frac{Q\left(a+b+c\right)}{4{\mathrm{\pi \epsilon }}_0\left(\mathrm{a}+{\mathrm{b}}^2+{\mathrm{c}}^2\right)}$

3. $\frac{Q\left(ab+bc+ca\right)}{12{\mathrm{\pi \epsilon }}_0\left(\mathrm{abc}\right)}$

4. $\frac{Q\left(a^2+b^2+c^2\right)}{4{\mathrm{\pi \epsilon }}_0\left({\mathrm{a}}^3+{\mathrm{b}}^3+{\mathrm{c}}^3\right)}$

Q. A particle of charge $q$ and mass $m$ moves rectilinearly under the action of an electric field, $E=4-2x$, where $x$ is a distance from the point where the particle was initially at rest. Calculate the distance travelled by the particle till it comes to rest.

1. $1\text{m}$
2. $2\text{m}$
3. $3\text{m}$
4. $4\text{m}$

Q. A simple pendulum of length $l$ has a bob of mass $m$ with a charge $q$ on it. A vertical sheet with surface charge density $\sigma$ passes through the point of suspension $O$. At equilibrium, the string makes an angle $\theta$ with the vertical, then -

1. $\tan \theta =\frac{\sigma q}{2{ϵ}_{0}mg}$
2. $\tan \theta =\frac{\sigma q}{3{ϵ}_{0}mg}$
3. $\tan \theta =\frac{2\sigma q}{{ϵ}_{0}mg}$
4. $\tan \theta =\frac{3\sigma q}{{ϵ}_{0}mg}$

Q. 1. A toy car with charge q moves on a frictionless horizontal plane surface under the influence of a uniform electric field E . Due to the force q E , its velocity increases from 0 to 6 m/s in one second duration. At that ins†an t 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) 2 m/s, 4 m/s (2) 1 m/s, 3 m/s (3) 1.5 m/s, 3 m/s (4) 1 m/s, 3.5 m/s

Q. The electric field in a region is given by: $\overrightarrow{E}=\left(4axy\sqrt{z}\right)\hat{i}+\left(2a{x}^2\sqrt{z}\right)\hat{j}+\left(\frac{a{x}^{2}y}{\sqrt{z}}\right)\hat{k}$ , where $a$ is a positive constant. The equation of an equipotential surface will be of the form

1. $z=\frac{\text{constant}}{\left[x^2{y}^2\right]}$
2. $z=\frac{\text{constant}}{\left[x{y}^2\right]}$
3. $z=\frac{\text{constant}}{\left[x^4{y}^2\right]}$
4. None

Q.

Equipotential surfaces cannot ________.

Q. There are two metallic plates of a parallel plate capacitor. One plate is given a charge $+q$ while the other plate is earthed as shown. For points $P,P_1$ and $P_2$ , the electric field intensity is non-zero at:

1. $P$
2. $P_1$
   
3. $P_2$
   
4. $P,P_1$ and $P_2$

Q. There is an insulator of length $L$ and of negligible mass with two small balls of mass $m$ and electric charge $q$ attached to its ends. The rod can rotate in the horizontal plane around a vertical axis crossing it at a distance $\frac{L}{4}$ from one of its ends. A uniform electric field $E$ exists in the region as shown in the figure. Find the time period for the small oscillations of the rod.

1. $T=2\pi \sqrt{\frac{4qE}{5mL}}$
2. $T=2\pi \sqrt{\frac{5mL}{4qE}}$
3. $T=2\pi \sqrt{\frac{mL}{5qE}}$
4. $T=2\pi \sqrt{\frac{3mL}{2qE}}$

Q. Figure shows a large conducting ceiling having uniform charge density $\sigma$ below which a charge particle of charge $q_0$ and mass m is hung from point O, through a small string of length $L$. Calculate the minimum horizontal velocity v required for the string to become horizontal.

1. $v=\sqrt{\frac{2mgl+2q_0\times \frac{\sigma }{2{ϵ}_0}\times L}{m}}$
2. $v=\sqrt{\frac{2mgl+2q_0\times \frac{\sigma }{2{ϵ}_0}\times L}{m}}$
3. $v=\sqrt{\frac{2mgl+2q_0\times \frac{\sigma }{2{ϵ}_0}\times L}{m}}$
4. $v=\sqrt{\frac{2mg{l}^2+2q_0\times \frac{\sigma }{2{ϵ}_0}\times L^2}{m{L}^2}}$

Q. Two small spheres each having the charge + q are suspended by insulating threads of length L from a hook. This arrangement is taken in space where there is no gravitational effect, then the angle between the two suspensions and the tension in each will be

1. ${180}^{\circ },\frac{1}{4\pi {ϵ}_0}\frac{Q^2}{(2L{)}^2}$
2. ${90}^{\circ },\frac{1}{4\pi {ϵ}_0}\frac{Q^2}{L^2}$
3. ${180}^{\circ },\frac{1}{4\pi {ϵ}_0}\frac{Q^2}{2L^2}$
4. ${180}^{\circ },\frac{1}{4\pi {ϵ}_0}\frac{Q^2}{L^2}$

Q.

A non-conducting square sheet of side 10 m is charged with a uniform surface charge density, $\sigma =-60\frac{\mu C}{m^2}$ . Find the magnitude and orientation of electric field vector due to the sheet at a point which is d = 0.02 mm away from the midpoint of the sheet.

1. 3.39 x 10⁶ N/C, away from the sheet

2. 6.78 x 10⁶ N/C, towards the sheet

3. 3.39 x 10⁶ N/C, towards the sheet

4. 6.78 x 10⁶ N/C, away from the sheet

Q. Electric field due to an infinite sheet of charge having surface density $\sigma$ is $E$. Electric field due to an infinite conducting sheet of same surface density of charge is

1. $E/2$
2. $E$
3. $2E$
4. $4E$

Q. Two parallel infinite line charges with linear charge densities $+\lambda C/m$and $–\lambda C/m$ are placed at a distance of $2R$ in free space. What is the electric field mid-way between the two line charges ?

1. 0 $N/C$
2. $\frac{2\lambda }{\pi {\epsilon }_{0}R}N/C$
3. $\frac{\lambda }{\pi {\epsilon }_{0}R}N/C$
4. $\frac{\lambda }{2\pi {\epsilon }_{0}R}N/C$

Q. A hollow disk of inner radius R and outer radius 2R is uniformly charged to charge Q and is rotating at angular velocity $\omega$ as shown in figure. Magnitude of magnetic dipole moment is

1. $Q\omega R^2$
2. $\frac{Q\omega R^2}{2}$
3. $\frac{2}{3}Q\omega R^2$
4. $\frac{5}{4}Q\omega R^2$

Q. In a region of space, the electric field is given by $\overrightarrow{E}=8\hat{i}+4\hat{j}+3\hat{k}$. The electric flux through a surface of area of $100\text{units}$ in $x-y$ plane is

1. $400\text{units}$
2. $800\text{units}$
3. $300\text{units}$
4. $1500\text{units}$

Q. In a region of space, the electric field is given by $\overrightarrow{E}=8\hat{i}+4\hat{j}+3\hat{k}$. The electric flux through a surface of area of $100\text{units}$ in $x-y$ plane is

1. $800\text{units}$
2. $300\text{units}$
3. $400\text{units}$
4. $1500\text{units}$

Q. (i) Identify the part of the electromagnetic spectrum which is :
(a) suitable for radar system used in aircraft navigation,
(b) produced by bombarding a metal target by high speed electron.
(ii) Why does a galvanometer show a momentary deflection at the time of charging or discharging a capacitor ? Write the necessary expression to explain this observation.

Q. Three point charge $q,-4q,2q$ are placed at the vertices of equilateral $\Delta$ ABC of side ${}^{\prime }{l}^{\prime }$ as shown in figure. Obtain the expression for the magnitude of the resultant electric force acting on the charge $q$.