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

1. \(q\times 2a\)

2. \(2q \times 2a\)

3. \(q\times a\)

4. \(2\times (2q\times 2a)\)

The ratio of the electric flux linked with shell \(A\) and shell \(B\) in the diagram shown below is:

An electric dipole is kept at the origin as shown in the diagram. The point \(A, B, C\) are on a circular arc with the centre of curvature at the origin. If the electric fields at \(A, B\) and \(C\) respectively are \(\vec E_1,\vec E_2,\vec E_3,\) then which of the following is incorrect? \(\left ( d\gg l \right )\)

        
1. \(\vec E_1=-\vec E_3\)
2. \(\vec E_1=-2\vec E_2\)
3. \(\vec E_1=\vec E_3\)
4. \(\vec E_3=-2\vec E_2\)

A large non-conducting sheet S is given a uniform charge density. Two uncharged small, metal rods A and B are placed near the sheet as shown in the following diagram. Choose the incorrect option:

1.  S attracts A.

2.  S attracts B.

3.  A attracts B.

4.  S repels A.

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

The electric flux from a cube of edge \(l\) is \(\phi\). What will be its value if the edge of the cube is made \(2l\) and the charge enclosed is halved?
1. \(\frac{1}{2}\phi\)
2. \(2\phi\)
3. \(4\phi\)
4. \(\phi\)

A charged particle \(q\) of mass \(m\) is released on the \(y\text-\)axis at \(y=a\) in an electric field \(\vec E = -4y \hat{j}.\) The speed of the particle on reaching the origin will be:
1. \(\sqrt{\frac{2 a}{m q}}\)
2. \(\frac{a}{\sqrt{m q}}\)
3. \(2 a \sqrt{\frac{q}{m}}\)
4. \(2 \sqrt{\frac{a}{m q}}\)

A point charge \(q\) is placed at the center of the open face of a hemispherical surface as shown in the figure. The flux linked with the surface is:

1. zero
2. \(\frac{q}{2\varepsilon_0}\)
3. \(\frac{q}{\varepsilon_0}\)
4. \(q \pi r^2\)

Four charges are arranged at the corners of a square \(ABCD\) as shown in the figure. The force on a positive charge kept at the center of the square is: