An electric dipole is in unstable equilibrium in the uniform electric field. The angle between its dipole moment and the electric field is

1.  \(90^{\circ}\)

2.  \(120^{\circ}\)

3.  \(0^{\circ}\)

4.  \(180^{\circ}\)

An electric dipole of dipole moment p is placed in an electric field of intensity E such that angle between electric field and dipole moment is $\theta$. Assuming that the potential energy of the dipole is zero when $\theta =0°$, the potential energy of the dipole will be

1. -pE cos$\theta$

2. pE(1-cos$\theta$)

3. pE(cos$\theta$-1)

4. -2pE(cos$\theta$-1)

Eight dipoles of charges of magnitude \((e)\) are placed inside a cube. The total electric flux coming out of the cube will be: 
1. \(\frac{8e}{\epsilon _{0}}\)
2. \(\frac{16e}{\epsilon _{0}}\)
3. \(\frac{e}{\epsilon _{0}}\)
4. zero

An electric dipole is situated in an electric field of uniform intensity E whose dipole moment is p and moment of inertia is I. If the dipole is displaced slightly from the equilibrium position, then the angular frequency of its oscillations is?

1. ${\left(\frac{{\displaystyle pE}}{{\displaystyle I}}\right)}^{1/2}$

2. ${\left(\frac{{\displaystyle pE}}{{\displaystyle I}}\right)}^{3/2}$

3. ${\left(\frac{{\displaystyle I}}{{\displaystyle pE}}\right)}^{1/2}$

4. ${\left(\frac{{\displaystyle p}}{{\displaystyle IE}}\right)}^{1/2}$

Two-point charges \(+q\) and \(–q\) are held fixed at \((–d, 0)\) and \((d, 0)\) respectively of a \((x, y)\) coordinate system. Then:

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:

Two short dipoles are placed at a certain distance exert a force 'F' on each other. If the distance between them is doubled then the force will become

1.  F

2.  $\frac{F}{4}$

3.  4F

4.  $\frac{F}{16}$

The net dipole moment of the system is of the magnitude:
          

1. \(q\times 2a\)

2. \(2q \times 2a\)

3. \(q\times a\)

4. \(2\times (2q\times 2a)\)

A point charge \(+q\) is kept at the center of the curvature of thin semicircular wire of length \(l\) as shown. The wire has uniformly distributed charge \(-q\) on it. The dipole moment of the system is

                  
1. \(\dfrac{2ql}{\pi^2}\)
2. \(\dfrac{2ql}{\pi}\)
3. \(\dfrac{\pi ql}{2}\)
4. zero

An electric dipole is placed at the centre of a sphere. Which of the following statements is correct?