Dipoles

Q. Three point charges $+q$, $-2q$ and $+q$ are placed at $(x=0,y=a,z=0)$, $(x=0,y=0,z=0)$ and $(x=a,y=0,z=0)$ respectively. The magnitude and direction of the electric dipole moment vector for the given system of charges are

1. $\sqrt{2}qa$ along $+x$ direction
2. $\sqrt{2}qa$ along $+y$ direction
3. $\sqrt{2}qa$ along the line joining points $(x=0,y=0,z=0)$ and $(x=a,y=a,z=0)$
4. $qa$ along the line joining points $(x=a,y=0,z=0)$ and $(x=a,y=a,z=0)$

Q. Three particles, each of mass $m$ and carrying a charge $q$ are suspended from a common point by insulating massless strings, each of length $L$. If the particles are in equilibrium and are located at the corners of an equilateral triangle of side $a$, then calculate the charge $q$ on each particle.
[Assume $L>>a$].

1. ${\left[\frac{4\pi {ϵ}_0{a}^{3}mg}{3L}\right]}^{\frac{1}{3}}$
2. ${\left[\frac{4\pi {ϵ}_0{a}^{3}mg}{3L}\right]}^{\frac{1}{2}}$
3. ${\left[\frac{2\pi {ϵ}_0{a}^{3}mg}{3L}\right]}^{\frac{1}{2}}$
4. None

Q. Which of the following graph of electrostatic force between two positive charges $\left(F_e\right)$ vs $r^2$, is a correct representation?
($r$ is the distance between two charges)

1. 
2. 
3. 
4. 

Q. A semi circular ring of radius R as shown in figure has charge per unit length $\lambda ={\lambda }_{0}cos\theta$. Electric dipole moment of this ring is.

1. $\lambda R^2$
2. $2\lambda R^2$
3. $\frac{\lambda R^2}{2}$
4. $\frac{3}{2}\lambda R^2$

Q. A point negative charge $-Q$ is placed at a distance $r$ from a dipole with dipole moment $P$ in the $\text{x-y}$ plane as shown in figure

The $\text{x-}$component of force acting on the charge $-Q$ is

1. $-\frac{PkQ}{r}\cos \theta \hat{i}$

2. $\frac{PkQ}{r}\cos \theta \hat{i}$

3. $-\frac{2PkQ}{r^3}\cos \theta \hat{i}$

4. $\frac{2PkQ}{r^3}\cos \theta \hat{i}$

Q. Charges $-q$ and $+q$ located at $A$ and $B$ respectively, constitute an electric dipole. Distance $AB=2a$, $O$ is the mid point of the dipole and $OP$ is perpendicular to $AB$. A charge $Q$ is placed at $P$ where $OP=y$ and $y>>2a$. The charge $Q$ experiences an electrostatic force $F$. If $Q$ is now moved along the equatorial line to $P^{\prime }$ such that $O{P}^{\prime }=\left(\frac{y}{3}\right)$, the force on $Q$ will be close to
Here $(\frac{y}{3}>>2a)$

1. $3F$
2. $\frac{F}{3}$
3. $9F$
4. $27F$

Q. The magnitude of electric field intensity at point $\text{P}(2,0,0)$ due to a dipole of dipole moment, $\overrightarrow{p}=\hat{i}+\sqrt{3}\hat{j}$ kept at origin is -

$($Assume that the point $\text{P}$ is at large distance from the dipole and $K=\frac{1}{4\pi {ϵ}_0})$

1. $\frac{\sqrt{7}K}{4}$
2. $\frac{\sqrt{7}K}{8}$
3. $\frac{\sqrt{13}K}{4}$
4. $\frac{\sqrt{15}K}{4}$

Q. Two positive charges $(+10\text{C})$ are kept on the arc of a circle and a negative charge $(-20\text{C})$ at the origin (centre of circle). Find the magnitude of net dipole moment for the given system.

1. $59.3\text{C-m}$
2. $69.3\text{C-m}$
3. $79.3\text{C-m}$
4. $89.3\text{C-m}$

Q. A point charge Q is placed just outside a cube of side 'a' near corner H. Flux of electric field associated with face ABCD is

1. $0$
2. $\frac{Q}{4{\epsilon }_0}$
3. $\frac{Q}{24{\epsilon }_0}$
4. $\frac{Q}{8{\epsilon }_0}$

Q. A point dipole of dipole moment $p$ is placed along $y$-axis, a point charge is placed at $x$-axis at distance $r$ from point dipole, find net force on dipole due to point charge.

1. $\frac{2kp}{r^3}{q}_0\hat{j}$
2. $\frac{kp}{r^3}{q}_0\hat{j}$
3. $\frac{kp}{r^3}{q}_0\hat{j}$
4. zero because total charge on dipole is zero.

Q. Three charges are arranged on the vertices of an equilateral triangle as shown in figure. Find the magnitude of dipole moment of the combination.

1. $\sqrt{2}qd$
2. $\sqrt{3}qd$
3. $\sqrt{5}qd$
4. $\sqrt{6}qd$

Q. Two infinitely long static line charge of constant positive line charge density $\lambda$ are kept parallel to each other. If a point charge $+q$ is kept in equilibrium between them and is given small displacement along $x-$ axis about its equilibrium position then the correct statement is
[Charge $+q$ is confined to move in the $x$ direction only]

1. Charge executes simple harmonic motion
2. Charge contines to move in the direction of its displacement
3. Charge takes circular path
4. Charge takes parabolic path

Q. . A positively charged thin metal ring of radius R is fixed in x-y plane with its centre at the originA negatively charged particle P is released from rest at the point (0, 0, Z.). Then the motion of Pis(a) periodic for all values of Z, (b) SHM for all values of Z, satisfying 0 > R(d) None of the above

Q. Two pith balls carrying equal charges are suspended from a common point by strings of equal length, the equilibrium separation between them is $r$. Now the strings are rigidly clamped at half the height. The equilibrium separation between the balls now becomes-

1. $\left(\frac{2r}{3}\right)$
2. ${\left(\frac{r}{\sqrt{2}}\right)}^2$
3. $\left(\frac{r}{\sqrt[3]{32}}\right)$
4. $\left(\frac{2r}{\sqrt{3}}\right)$

Q. Find the electric field at the centre of a uniformly charged semicircular ring of radius R and linear charge density $\lambda$ :

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

Q. A thin Non-conducting rod is bent into a semicircle of radius $r$. A charge $+Q$ is uniformly distributed along the upper half and a charge $-Q$ is uniformly distributed along the lower half, as shown in figure. Find the electric field $E$ at $\text{P}$.

1. $\frac{4Q}{{\pi }^2{ϵ}_0{r}^2}$
2. $\frac{2Q}{{\pi }^2{ϵ}_0{r}^2}$
3. $\frac{Q}{4{\pi }^2{ϵ}_0{r}^2}$
4. $\frac{Q}{{\pi }^2{ϵ}_0{r}^2}$

Q. Statement I: Dipole is a scalar Quantity.
Statement II: Dipole is a vector Quantity.

1. Statement I – False
   ​Statement II - True
   
2. Statement I – True
   ​Statement II - False
   
3. Statement I – True
   Statement II - True
   
4. Statement I – False
   ​Statement II - False
   

Q. The electric field at the centre of a uniformly charged ring is zero. What is the electric field at the centre of a half ring if the charge on it be Q and its radius be R?

1. $\frac{1}{4\pi {\epsilon }_0}\frac{Q}{\pi R^2}$
2. $\frac{1}{4\pi {\epsilon }_0}\frac{Q}{R^2}$
3. $\frac{1}{4\pi {\epsilon }_0}\frac{2Q}{\pi R^2}$
4. $\frac{1}{4\pi {\epsilon }_0}\frac{2Q}{R^2}$

Q. Electrostatic force $F$ on a charge $\frac{Q}{2}$ at an axial point due to a finite line charge varies as $F=\frac{18000}{x^2+4x}$, where $x$ is in metres and is the distance along axial line from one of the ends. The total charge on the line is

1. $2\text{C}$
2. $0.02\text{C}$
3. $0.002\text{C}$
4. $0.004\text{C}$

Q. Three charges are arranged on the vertices of an equilateral triangle as shown in figure. Find the dipole moment of the combination.

Q. A thin semi-circular ring of radius $r$ has a positive charge $q$ distributed uniformly over it. The net electric field $\overrightarrow{E}$ at the centre $O$ is :

1. $\frac{q}{4{\pi }^2{ϵ}_0{r}^2}\overrightarrow{j}$
2. $-\frac{q}{4{\pi }^2{ϵ}_0{r}^2}\overrightarrow{j}$
3. $-\frac{q}{2{\pi }^2{ϵ}_0{r}^2}\overrightarrow{j}$
4. $\frac{q}{2{\pi }^2{ϵ}_0{r}^2}\overrightarrow{j}$

Q. In the given diagram, force acting on the conductor $\text{OA}$, aligned along the body digonal of the cube, is:
( Given, side of the cube is $2\text{m},I=2\text{A},\overrightarrow{B}=3\hat{k}\text{T}$ )

1. $6(\hat{i}+\hat{j})\text{N}$
2. $3(\hat{i}+\hat{j})\text{N}$
3. $(\hat{i}+\hat{j})\text{N}$
4. $12(\hat{i}+\hat{j})\text{N}$

Q. Three point charges $+q,-2q$ and $+q$ are placed at points $(x=0,y=a,z=0),(x=0,y=0,z=0)$ and $(x=a,y=0,z=0)$ respectively. The magnitude and direction of the electric dipole moment vector of this charge assembly are:

1. $\sqrt{2}qa$ along $+y$ direction
2. $\sqrt{2}qa$ along the line joining points $(x=0,y=0,z=0)$ and $(x=a,y=a,z=0)$
3. $qa$ along the line joining points $(x=0,y=0,z=0)$ and $(x=a,y=a,z=0)$
4. $\sqrt{2}qa$ along $+x$ direction

Q. Three charges are arranged on the vertices of an equilateral triangle, as shown in the figure. Find the dipole moment of the combination.

Q. Two identical electric point dipoles have dipole moments $\overrightarrow{P_1}=P\hat{i}\text{and}\overrightarrow{P_2}=-P\hat{i}$ and held on the $x-$ axis at distance ${}^{\prime }{a}^{\prime }$ from each other. When released, they move along $x-$ axis with the direction of their dipole moments remaining unchanged. If the mass of each dipole is ${}^{\prime }{m}^{\prime }$, their speed
when they are infinitely far apart is :

1. $\frac{P}{a}\sqrt{\frac{1}{\pi {\epsilon }_{0}ma}}$
2. $\frac{P}{a}\sqrt{\frac{1}{2\pi {\epsilon }_{0}ma}}$
3. $\frac{P}{a}\sqrt{\frac{2}{\pi {\epsilon }_{0}ma}}$
4. $\frac{P}{a}\sqrt{\frac{3}{2\pi {\epsilon }_{0}ma}}$

Q. Under what condition an electron moving through a magnetic field experiences the maximum force?

Q. A uniform electric field $E$ is created between two parallel, charged plates as shown in figure. An electron enters the field symmetrically between the plates with a speed $v_0$. The length of each plate is $l$. Find the angle of deviation of the path of the electron as it comes out of the field.

1. ${\tan }^{-1}\frac{ml}{E{v_0}^2}$
2. ${\tan }^{-1}\frac{El}{em{v}_0}$
3. ${\tan }^{-1}\frac{eEl}{m{v_0}^2}$
4. ${\tan }^{-1}\frac{El}{m{v_0}^2}$

Q. A thin semi-circular ring of radius $R$ has a positive charge $q$ distributed uniformly over it. The net field $\overrightarrow{E}$ at the centre $O$ is:

1. $\frac{q}{4{\pi }^2{\epsilon }_0{R}^2}\hat{j}$
2. $-\frac{q}{4{\pi }^2{\epsilon }_0{R}^2}\hat{j}$
3. $-\frac{q}{2{\pi }^2{\epsilon }_0{R}^2}\hat{j}$
4. $\frac{q}{2{\pi }^2{\epsilon }_0{R}^2}\hat{j}$

Q. Two charged conducting spheres of radii $R_1$ and $R_2$ . separated by a large distance. are connected by a long wire. The ratio of the charges on them is

1. $\frac{R_1}{R_2}$
2. $\frac{R_2}{R_1}$
3. $\frac{R_1^2}{R_7^2}$
4. $\frac{R_2^2}{R_1^2}$

Q. A thin non-conducting ring of radius $R$ has a linear charge $\lambda ={\lambda }_0\cos \theta$ where ${\lambda }_0$ is the value of $\lambda$ at $\theta =0$ . The net electric dipole moment for this charge distribution is :

1. $\pi R^2/{\lambda }_0$
2. ${\lambda }_0/\pi R^2$
3. $\pi R^2{\lambda }_0$
4. $\frac{{\lambda }_0\pi }{R^2}$