Electric Field Due to a Dipole

Q. A particle of mass $1\text{mg}$ and charge $q$ is lying at the mid-point of two stationary particles kept at a distance $2\text{m}$, when each is carrying same charge ${}^{\prime }{q}^{\prime }.$ If the free charged particle is displaced from its equilibrium position through distance ${)}^{\prime }{x}^{\prime }(x<<1\text{m}).$ The particle executes SHM. Its angular frequency of oscillation will be____ $\times {10}^8\text{rad/s}$ if $q^2=10{\text{C}}^2$.

Q.

Two electric dipoles of moment P and 64 P are placed in opposite direction on a line at a distance of 25 cm. The electric field will be zero at point between the dipoles whose distance from the dipole of moment P is

1. 5 cm
2. 
3. 10 cm
4. 

Q. Four point charges +q, +q, -q and -q are placed on the corners of a square of side length ${}^{\prime }{a}^{\prime }$ as shown in the figure. Magnitude of electric field at a point which is at a distance $x$(>>$a$) from the centre along a line perpendicular to the plane of square and passing through the center is

1. $\frac{\sqrt{2}qa}{4\pi {\epsilon }_0{x}^3}$
2. $\frac{qa}{2\pi {\epsilon }_0{x}^3}$
3. $\frac{\sqrt{2}qa}{2\pi {\epsilon }_0{x}^3}$
4. $\frac{qa}{4\pi {\epsilon }_0{x}^3}$

Q. A particle of mass $m$ and charge $+q$ is midway between two fixed charged particles, each having a charge $+q$ and at a distance $2L$ apart. The middle charge is displaced slightly along the line joining the fixed charges and released. The time period of oscillation is proportional to

1. $L^{1/2}$
2. $L$
3. $L^{3/2}$
4. $L^2$

Q. Three identical dipoles are arranged as shown below. What will be the net electric field at P? $(K=\frac{1}{4\pi {ϵ}_0})$

1. $\frac{k.p}{x^3}$
2. $Zero$
3. $\frac{2kp}{x^3}$
4. $\frac{\sqrt{2}kp}{x^3}$

Q.

An electric dipole is placed along the x - axis at the origin O . A point P is at a distance of 20cm from this origin such that OP makes an angle $\frac{\pi }{3}$ with the x-axis. If the electric field at P makes an angle θ with the x-axis, the value of $\theta$ would be:

1. $\frac{\pi }{3}$
   
2. $\frac{\pi }{3}+ta{n}^{-1}\frac{\sqrt{3}}{2}$
3. $\frac{2\pi }{3}$
4. $ta{n}^{-1}\frac{\sqrt{3}}{2}$
   

Q. The dependence of electric potential $V$ on the distance ${}^{\prime }{r}^{\prime }$ from the centre of a charged spherical shell is shown by

1. 
2. 
3. 
4. 

Q.

Explain the equatorial field or electric field on the equatorial line of an electric dipole that is?

Q. A point charge$(+10\text{nC})$ is kept at point $P(1,2,3)$ and a test charge is kept at point $Q(3,4,5)$. Find the electric field experienced by the test charge.
$[$Assume distances in metre$]$

1. $2.2(\hat{i}+\hat{j}+\hat{k})\text{N/C}$
2. $3.3(\hat{i}+\hat{j}+\hat{k})\text{N/C}$
3. $4.4(\hat{i}+\hat{j}+\hat{k})\text{N/C}$
4. $5.5(\hat{i}+\hat{j}+\hat{k})\text{N/C}$

Q. A point charge $4\mu C$ is at the centre of a cubical Gaussian surface of 10 cm edge. Net electric flux through the surface is:

1. $2.5\times {10}^{5}N{m}^2{C}^{-1}$
2. $4.5\times {10}^{5}N{m}^2{C}^{-1}$
3. $4.5\times {10}^{6}N{m}^2{C}^{-1}$
4. $2.5\times {10}^{6}N{m}^2{C}^{-1}$

Q. Consider two concentric spherical surfaces ${\text{S}}_1$ with radius $a$ and ${\text{S}}_2$ with radius $2a$, both centred on the origin. There is a charge $+q$ at the origin, and no other charges. Compare the flux ${\varphi }_1$ through ${\text{S}}_1$ with flux ${\varphi }_2$ through ${\text{S}}_2$

1. ${\varphi }_1=4{\varphi }_2$
2. ${\varphi }_1=2{\varphi }_2$
3. ${\varphi }_1={\varphi }_2$
4. ${\varphi }_1=\frac{{\varphi }_2}{2}$

Q.

Two parallel large thin metal sheets have equal surface charge densities $\left(\sigma =26.4\times {10}^{-12}\mathrm{c}/{\mathrm{m}}^2\right)$ of opposite signs. The electric field between these sheets is

1. $1.5\mathrm{N}/\mathrm{c}$

2. $3\mathrm{N}/\mathrm{c}$

3. $1.5\times {10}^{-10}\mathrm{N}/\mathrm{c}$

4. $3\times {10}^{-10}\mathrm{N}/\mathrm{c}$

Q. Figure shows three concentric spherical conducting shells A, B, and C of radii $R,2R$ and $4R$ respectively. Shells $A$ and $C$ are connected by a conducting wire and B is given charge $Q$. $[\text{Consider}\frac{1}{4\pi {ϵ}_0}=K]$
Match the following columns:

$\begin{array}{cc}\text{Column-I}& \text{Column-II}\\ \text{A. Charge on shell A}& \left(p\right)\frac{Q}{3}\\ \text{B. Charge on shell C}& \left(q\right)-\frac{Q}{3}\\ \text{C. Potential of shell A}& \left(r\right)Q\\ \text{D. Potential of shell C}& \left(s\right)\frac{KQ}{4R}\\ & \left(t\right)\text{None}\end{array}$

1. $A-s,B-t,C-q,D-p$
2. $A-p,B-q,C-s,D-t$
3. $A-q,B-p,C-s,D-s$
4. $A-p,B-s,C-q,D-s$

Q. Two point charges $q_1$ and $q_2$ having charge$q_1=+16\mu \text{C}$ and $q_2=+4\mu \text{C}$, are separated in vacuum by a distance of $3.0\text{m}$. Find the point on the line joining these charges where the net electric field is zero.

1. $2\text{m}$ from $q_1$
2. $1\text{m}$ from $q_1$
3. $2\text{m}$ from $q_2$
4. $1.5\text{m}$ from $q_2$

Q.

Gauss’s law is defined and valid only for a closed surface.

1. True

2. false

Q. Two charges of $+25$ x ${10}^{-9}$ coulomb and $-25$ x ${10}^{-9}$ coulomb are placed $6$ m apart. Find the electric field intensity ratio at points $4$ m from the centre of the electric dipole
(i) on axial line
(ii) on equatorial line

1. $\frac{1000}{49}$
2. $\frac{49}{1000}$
3. $\frac{500}{49}$
4. $\frac{49}{500}$

Q.

Which of the following set have different dimensions?

1. Pressure, Young’s modulus, Stress

2. EMF, Potential difference, Electric potential

3. Heat, Work done, Energy

4. Dipole moment, Electric flux, Electric field

Q.

A water molecule has a permanent electric dipole moment of magnitude 6 x 10^-30 C-m. estimate the size of the electric field produces at the position of a neighbouring water molecule which is 3 x 10^-9 m away

Q. The variation of electric field between two charges $q_1$ and $q_2$ along the line joining the charges is plotted against distance from $q_1$ (taking rightward direction of electric field as positive) as shown in the figure. Then, the correct statement is

1. $q_1$ and $q_2$ are positive and $q_1<q_2$
2. $q_1$ and $q_2$ are positive and $q_1>q_2$
3. $q_1$ is positive and $q_2$ is negative ; $q_1<\left|q_2\right|$
4. $q_1$ and $q_2$ are negative and $\left|q_1\right|<\left|q_2\right|$

Q. Eight charges, 1 μC, -7 μC, -4 μC, 10 μC, 2 μC, -5 μC, -3 μC and 6 μC are situated at the eight corners of the cube of side 20 $cm$. A spherical surface of 80 $cm$ radius encloses this cube. The centre of this sphere coincides with the center of the cube. Then, the total ongoing flux from the spherical surface (in units of $Vm$) is

1. $36\pi \times {10}^3$
2. $684\pi \times {10}^3$
3. zero
4. none of these

Q. Derive an expression for electric field due to an electric dipole at a point on its axial line.

Q. A quarter wire $\text{AB}$ of radius $R$, carrying a current $i$, is kept in a uniform magnetic field $\overrightarrow{B}$ as shown in the figure. Determine the magnitude of magnetic force acting on the wire?

1. $iRB$
2. $2iRB$
3. $\pi iRB$
4. $\sqrt{2}iRB$

Q. There is an electric field $E$ in $x-$ direction. If the work done by electric force on moving a charge of $0.2\text{C}$ through a distance of $2\text{m}$ along a line making an angle ${60}^{\circ }$ with $x-$ axis is $4\text{J}$, then what is the value of $E$?
(Neglect gravity)

1. $10\text{N/C}$
2. $15\text{N/C}$
3. $20\text{N/C}$
4. $25\text{N/C}$

Q. A short electric dipole is held at the origin with its dipole moment along x axis . if electric fields intensity at a point( r, theta ) .in the dipole field 27v/m the electric field intensity at a point 3r, theta is

Q. A light rod is hinged (free to rotate) at its centre $O$ as shown in figure. Two point charges of same magnitude $+q$ are kept at its two ends. The rod is placed in uniform electric field $E$ as shown. Space is gravity free. The equilibrium is

1. stable
2. unstable
3. neutral
4. not in equilibrium

Q. a short dipole of dipole moment p=(root(5)i + j) c m is kept at origin .the magnitude of electric field intensity at point (0 m, 1 m) is root(N)/(4 pi epsilon not ). the value of N is ?

Q. The angle between the dipole moment and electric field at any point on the equatorial plane is :

1. $0^{\circ }$
2. ${90}^{\circ }$
3. ${180}^{\circ }$
4. ${45}^{\circ }$

Q. Two small identical electrical dipoles $AB$ and $CD$ each of dipole moment $\overrightarrow{p}$ are kept at an angle of ${120}^o$ as shown in the figure. What is the resultant dipole moment of this combination ? If this system is subjected to electric field $\left(\overrightarrow{E}\right)$ directed along $+X$ direction, what will be the magnitude and direction of the torque acting on this?

Q. A cavity of radius $r$ is present inside a fixed solid dielectric sphere of radius $R$, having a volume charge density of $\rho$. The distance between the centres of the sphere and the cavity is $a$. An electron is released inside the cavity at an angle $\theta ={45}^o$ as shown. The electron (of mass $m$ and charge $-e$) will take ${\left(\frac{P\sqrt{2}mr{\epsilon }_0}{ea\rho }\right)}^{\frac{1}{2}}$ time to touch the sphere again. Neglect gravity. Find the value of $P$ :

1. 2
2. 3
3. 6
4. 9

Q. There is uniformly charged non-conducting solod sphere made of material of dielectric constant 1. If electric potential at infinity be zero, then the potential at its surface is V. If we take electric potential at its surface to be Zero, then potential at centre will be a. 3V/2 b. V/2 c. V d. zero