Dipole Moment

Q.

A system has two charges $q_A=2.5\times {10}^{-7}Cand{q}_B=-2.5\times {10}^{-7}C$ located at points A(0, 0, -15cm) and B(0, 0, +15cm), respectively. What are the total charge and electric dipole moment of the system?

Q. Three charges $Q,+q$ and $+q$ are placed at the vertices of a right angled isosceles triangle as shown in figure. The net electrostatic energy of the configuration is zero, if $Q$ is equal to

1. $\frac{-q}{1+\sqrt{2}}$
2. $-2q$
3. $\frac{-\sqrt{2}q}{1+\sqrt{2}}$
4. $+q$

Q.

Consider the force $F$ on a charge $q$ due to a uniformly charged spherical shell of radius $R$ carrying charge $Q$ distributed uniformly over it. Which one of the following statements is true for $F$, if $q$ is placed at distance $r$ from the center of the shell?

1. $F=\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{qQ}{R^2}>F>0forr<R$

2. $F=\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{qQ}{r^2}forr>R$

3. $F=\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{qQ}{r^2}forallr$

4. $F=\frac{1}{4{\mathrm{\pi \epsilon }}_0}\frac{qQ}{R^2}forr<R$

Q. An electric dipole is placed in an electric field generated by a point charge. Then

1. net electric force on the dipole must be zero
2. net electric force on the dipole may be zero
3. torque on the dipole due to the field must be zero
4. torque on the dipole due to the field may be zero

Q. An electric dipole is placed in a uniform electric field. The net electric force on the dipole

1. is always zero
2. depends on the orientation of the dipole
3. can never be zero
4. depends on the strength of the electric field

Q. A neutral water molecule $\left(H_{2}O\right)$ in its vapor state has an electric dipole moment of magnitude $6.4\times {10}^{–30}$ C-m. How far apart are the centres of positive and negative charge?

1. $4mm$
   
2. $4pm$
3. $4m$
   
4. $4\mu m$
   

Q. (a) Use Gauss' law to derive the expression for the electric field (E) due to a straight uniformly charged infinite line of charge density $\lambda$ C/m.
(b) Draw a graph to show the variation of E with perpendicular distance r from the line of charge.
(c) Find the work done in bringing a charge q from perpendicular distance $r_1$ to $r_2(r_2>r_1)$.

Q. The electric field due to an electric dipole at a distance $r$ from its center on the axial line is $E$. If the dipole is rotated through an angle of ${90}^{\circ }$ about its perpendicular axis, electric field at the same point will be

1. $\frac{E}{2}$
2. $E$
3. $2E$
4. $\frac{E}{4}$

Q.

Three charges are arranged on the vertices of an equilateral triangle as shown in figurre (29-E6). Find the eipole moment of the combination.

Q. A short dipole is placed at origin of coordinate system in $\text{x-y}$ plane as shown in figure. Find the electric field at point $\text{P}(0,y)$. $(y>>$ length of dipole$)$

1. $\frac{Kp}{2y^3}[-2\hat{i}-\hat{j}]$
2. $\frac{2Kp}{y^3}[-2\hat{i}-\hat{j}]$
3. $\frac{\sqrt{2}Kp}{y^3}[-\hat{i}-2\hat{j}]$
4. $\frac{Kp}{\sqrt{2}{y}^3}[-\hat{i}-2\hat{j}]$

Q. A ball of mass 1g and charge 10^{-8} C moves from point A, where potential is 600V to the point where potential is zero.Velocity of the ball at point B is 20cm/s.The velocity of the ball at point A will be a)22.8 cm/s b)228 cm/s c)16.8 cm/s d)168 cm/

Q.

Two charges $+3.2\times {10}^{-19}Cand-3.2\times {10}^{-19}C$ placed $2.4A^o$ apart form an electric dipole. It is placed in a uniform electric field of intensity $4\times {10}^5{Vm}^{-1}$ , the workdone to rotate the electric dipole from the equilibrium position by ${180}^o$ is ......$\times {10}^{-23}J$

Q. At a far away distance $r$ along the axis from an electric dipole, the electric field is $E$. Find the electric field at distance $2r$ along the perpendicular bisector.

1. -$\frac{E}{4}$
2. -$\frac{E}{16}$
3. $\frac{E}{2}$
4. $E$

Q. What is the angle between the electric dipole moment and the electric field strength due to it on the equatorial line

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

Q. A positive point charge $q$ is fixed at origin. A short dipole with a dipole moment $p$ is placed along the $x-$axis far away from the origin with $p$ pointing along the $+x-$axis. The kinetic energy of the dipole when it reaches distance $d$ from origin is

1. $\frac{3qp}{8\pi {ϵ}_0{d}^2}$
2. $\frac{qp}{4\pi {ϵ}_0{d}^2}$
3. $\frac{2qp}{4\pi {ϵ}_0{d}^2}$
4. $\frac{qp}{16\pi {ϵ}_0{d}^2}$

Q. Two short electric dipoles of moment $P$ and $27P$ are placed as shown below. If at the point $O$ the electric field is zero between the dipoles, then the distance of the point $O$ from the centre of first dipole is

1. $2\text{cm}$
2. $4\text{cm}$
3. $6\text{cm}$
4. $8\text{cm}$

Q. The magnitude of force due to an electric dipole of dipole moment $3.6\times {10}^{-29}\text{C-m}$ on an electron $25\text{nm}$ from the centre of the dipole along the dipole axis is

1. $6.6\times {10}^{-15}\text{N}$
2. $7.8\times {10}^{-15}\text{N}$
3. $9.4\times {10}^{-15}\text{N}$
4. $12\times {10}^{-15}\text{N}$

Q. Two identical electric dipoles are arranged on $x$-axis as shown in figure. Electric field at the origin will be ( Assume $\frac{1}{4\pi {ϵ}_0}=K$ )

1. zero
2. $\frac{Kp\sqrt{2}}{r^3}\hat{j}$
3. $\frac{-Kp\sqrt{2}}{r^3}\hat{j}$
4. $\frac{2Kp}{r^3}\hat{i}-\frac{kp}{r^3}\hat{j}$

Q.

Two particles, carrying charges - q and +q and having equal masses m each are fixed at the ends of a light rod of length a to form a dipole. The rod is clamped at an end and is placed in a uniform electric field E with slightly tilted and then released. Neglecting gravity find the time period of small oscillations.

Q. Point charges q, q, -2q are placed at the corners of an equilateral triangle ABC of side l. The magnitude of net electric dipole moment of the system is

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

Q. A short dipole is placed along $x-$ axis with centre at origin ($\text{O}$). The electric field at a point $\text{P}$ due to dipole such that $\overrightarrow{\text{OP}}$ makes an angle of ${45}^{\circ }$ with the $x-$ axis, is directed along a direction making

1. ${\tan }^{-1}\left(0.5\right)$ with $x-$ axis
2. $\frac{\pi }{4}+{\tan }^{-1}\left(0.5\right)$ with $x-$ axis
3. $\frac{\pi }{4}+{\tan }^{-1}\left(0.5\right)$ with $y-$ axis
4. ${\tan }^{-1}\left(0.5\right)$ with $y-$ axis

Q. Find the maximum value of torque acting on the dipole placed in a uniform electric field as shown in figure.

1. ${10}^{-6}\text{N-m}$
2. $2\times {10}^{-6}\text{N-m}$
3. $3\times {10}^{-6}\text{N-m}$
4. Data insufficient

Q. An electron and a proton are at a distance of $1\dot{A}$. The dipole moment will be $(C\times m)$

1. $1.6\times {10}^{19}$
2. $1.6\times {10}^{-29}$
3. $3.2\times {10}^{19}$
4. $3.2\times {10}^{29}$

Q.

Two particles A and B having oposite charges $2.0\times {10}^{-6}C$ and $-2.0\times {10}^{-6}C,$ are placed at a separation of 1.0 cm. (a) Write down te electric diple moment of this pair. (b) calculate the electric field at a Point on the axis of the dipole 1.0 m away from the centre. (c) Calculat the electric field at a point on the perpendicular bisector of the dipole and 1.0 m away from the centre.

Q. What is an electric dipole? Define electric dipole moment?

Q. The linear charge density upon the semicircular ring, on both side is same in magnitude i.e. µ but different in nature, what is the magnitude of electric field intensity at center?

Q.

For uniform electric field, field lines are _______

Q. Initially the capacitor is uncharged , find the charge on capacitor as a function of time, if switch is closed at $t=0$.

1. $q=\frac{\epsilon C}{2}(1-e^{\frac{-2t}{3RC}})$
2. $q=\frac{\epsilon C}{2}(1-e^{\frac{-t}{RC}})$
3. $q=\frac{\epsilon C}{2}(1-e^{\frac{-t}{2RC}})$
4. $q=\frac{3\epsilon C}{2}[1-e^{\left[\frac{-2t}{RC}\right]}]$

Q. A positive point charge $q$ is fixed at origin. a small dipole with a dipole moment $\overrightarrow{p}$ is placed along the x-axis far away from the origin with $\overrightarrow{p}$ pointing along positive $x$-axis. Find the kinetic energy of the dipole when it reaches a distance $d$ from the origin.

1. $\frac{qp}{4\pi {ϵ}_0{d}^2}$
2. $\frac{2qp}{\pi {ϵ}_0{d}^2}$
3. $\frac{qp}{2\pi {ϵ}_0{d}^2}$
4. $\frac{4qp}{\pi {ϵ}_0{d}^2}$

Q. in a spherical capacitor with plate radii a and b, the potential difference between the plates is V . the electric field between the plates at a radial dis†an ce r from the centre is