Dipole Moment

Q.

An electric dipole of moment vector $p=\left(-\hat{i}-3\hat{j}+2\hat{k}\right)\times {10}^{-29}cm$ is at the origin $\left(0,0,0\right)$. The electric field due to this dipole at$\begin{array}{l}\overrightarrow{r}=(\hat{i}+3\hat{j}+5\hat{k})\end{array}$ is parallel to [Note that $\overrightarrow{r}.\overrightarrow{p}=0$]

1. $\hat{i}-3\hat{j}-2\hat{k}$

2. $-\hat{i}-3\hat{j}+2\hat{k}$

3. $\hat{i}+3\hat{j}-2\hat{k}$

4. $-\hat{i}+3\hat{j}-2\hat{k}$

Q. Dimensional formula of torque is

बल-आघूर्ण का विमीय सूत्र है

1. [M¹L²T^–1]
   
2. [M¹L^–1T²]
   
3. [M¹L²T^–2]
   
4. [M¹L¹T^–2]
   

Q. Find the force on a diapole of moment p placed at a distance r from an infinitely charged rod of density $\lambda$.

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

Q. Two charges $+3.2\times {10}^{-19}$ and $-3.2\times {10}^{-19}$ C placed $2.4\dot{A}$ apart form an electric dipole. It is placed in a uniform electric field of intensity $4\times {10}^5$ volt/m. The electric dipole moment is

1. $15.36\times {10}^{-29}Coulomb\times m$
2. $15.36\times {10}^{-19}Coulomb\times m$
3. $7.68\times {10}^{-29}Coulomb\times m$
4. $7.68\times {10}^{-19}Coulomb\times m$

Q. Dipole moment is a vector directed from negative to the positive charge.

1. False
2. True

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

Q. The torque acting on a dipole of moment P in an electric field E is

1. Scalar Product of P and E
2. Vector product of P and E
3. zero
4. - (Vector product of P and E)

Q. Find the net force on a dipole of moment p placed on the arms of a ring of charge Q and radius R Assume x <<R.

1. Zero
2. $\frac{2kQp}{R^3}$
   
3. $\frac{kQp}{R^3}$
   
4. $\frac{\sqrt{2}kQp}{R^3}$

Q. Define the term electric dipole moment. Write its S.I unit. Is it a scalar quantity or vector quantity?

Q. Find the force on diapole p placed at a distance r from an onother dipole $p_0$

1. $4k{p}_{0}p/r^4$
2. $6k{p}_{0}p/r^4$
3. $5k{p}_{0}p/r^4$
4. $k{p}_{0}p/r^4$

Q. If the magnitude of intensity of electric field at a distance $x$ on axial line and at a distance $y$ on equatorial line for a given dipole are equal, then $x:y$ is

Q. Two charges of magnitude -4C and 4C are placed at points (1, 2, 3) and (3, 4, 2) respectively. What is the dipole moment?

1. $2\hat{i}-2\hat{j}-\hat{k}Cm$
2. $-8\hat{i}+8\hat{j}+4\hat{k}Cm$
3. $8\hat{i}+8\hat{j}-4\hat{k}Cm$
4. $12cm$

Q. What is the net dipole moment for the given arrangement.

1. $1.7\times {10}^{-2}Q$
2. $1.7\times {10}^{-3}Q$
3. $0.7Q$
4. $Zero$

Q. If the magnitude of intensity of electric field at a distance $x$ on axial line and at a distance $y$ on equatorial line for a given dipole are equal, then $x:y$ is

Q. A domain in a magnet is in the form of a cube of side length $1\mu \text{m}$. If it contains $8\times {10}^{10}$ atoms and each atomic dipole has a dipole moment of $9\times {10}^{-24}{\text{A-m}}^2$ and all of this dipoles are aligned in the same direction, then the magnetisation of the domain is:

Q. Find the force on diapole p placed at a distance r from an onother dipole $p_0$

1. $4k{p}_{0}p/r^4$
2. $6k{p}_{0}p/r^4$
3. $5k{p}_{0}p/r^4$
4. $k{p}_{0}p/r^4$

Q. There are two dipoles in space with dipole moment $\overrightarrow{P_1}=\hat{i}+2\hat{j}+\hat{k}$ $and$ $\overrightarrow{P_2}=2\hat{i}-3\hat{j}+\hat{k}$. What is the net dipole moment of the arrangement?

1. $-\hat{i}+5\hat{j}$
2. $3\hat{i}-j+2\hat{k}$
3. $\hat{i}-5\hat{j}$
4. $\frac{3\hat{i}-\hat{j}+2\hat{k}}{\sqrt{14}}$

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. $3.2\times {10}^{29}$