Dipoles

Q. A semi circular ring of radius $R$ as shown in figure has charge per unit length $\lambda ={\lambda }_o\cos \theta$. 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. 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. 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. Charges are placed on corners of square of side $a$ (as shown in figure). Find magnitude of net dipole moment.

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

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

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

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.