Dipole Moment

Q.

Is dipole moment a scalar or vector?

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. 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. Find the dipole moment of the system given below. The two oppositely.charged quater rings have the same magnitude of linear charge density $\lambda$

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

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. The electric field in a region is given by $\overrightarrow{E}=\alpha x\hat{i}$. Here, $\alpha$ is a positive constant of proper dimension. Find the total flux passing through a cube bounded by the coordinates, $x=l,x=2l,y=0,y=l,z=0,z=l.$

1. $3\alpha l^3$
2. $4\alpha l^3$
3. $\alpha l^3$
4. $2\alpha l^3$

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

Q. Dipole moment is a scalar quantity.

1. False
2. True

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. 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. Charge +q is uniformly distributed on a circular ring of radius R and a point charge -q is placed at a distance y from the center of the ring on its axis. The magnitude of dipole moment of this system is.
[where q = 2C and y = 3m, R = 4m]

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. $k{p}_{0}p/r^4$