Q. No.| 1. | \(8~\text{mC}\) | 2. | \(2~\text{mC}\) |
| 3. | \(5~\text{mC}\) | 4. | \(7~\mu \text{C}\) |
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 |
An electric dipole is placed at the centre of a sphere. Which of the following statements is correct?
| 1. | The electric flux through the sphere is zero. |
| 2. | The electric field is zero at every point on the sphere. |
| 3. | The electric field is zero at every point inside the sphere. |
| 4. | The electric field is uniform inside the sphere. |
The net dipole moment of the system is of the magnitude:
1. \(q\times 2a\)
2. \(2q \times 2a\)
3. \(q\times a\)
4. \(2\times (2q\times 2a)\)
| 1. | \(10^{-2}~\text{N-m}\) |
2. | \(0\) |
| 3. | \(10^{-1}~\text{N-m}\) |
4. | \(0.01~\text{N-m}\) |
The electric field at the equator of a dipole is \(E.\) If the strength of the dipole and distance are now doubled, then the electric field will be:
| 1. | \(E/2\) | 2. | \(E/8\) |
| 3. | \(E/4\) | 4. | \(E\) |
(\(r\gg\) separation of two charges forming the dipole, \(\varepsilon_{0} =\) permittivity of free space)
1. \(\overrightarrow{E}=\dfrac{\overrightarrow{P}}{4\pi \varepsilon _{0}r^{3}}\)
2. \(\overrightarrow{E}=\dfrac{2\overrightarrow{P}}{\pi \varepsilon _{0}r^{3}}\)
3. \(\overrightarrow{E}=-\dfrac{\overrightarrow{P}}{4\pi \varepsilon _{0}r^{2}}\)
4. \(\overrightarrow{E}=-\dfrac{\overrightarrow{P}}{4\pi \varepsilon _{0}r^{3}}\)
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. \(\vec E_3=-2\vec E_2\)
The figure shows electric field lines in which an electric dipole \(p\) is placed as shown in the figure. Which of the following statements is correct?
| 1. | The dipole will not experience any force. |
| 2. | The dipole will experience a force towards the right. |
| 3. | The dipole will experience a force towards the left. |
| 4. | The dipole will experience a force upwards. |
Two point dipoles of dipole moment \(\vec{p}_{1}\) and \(\vec{p}_{2}\) are at a distance \(x\) from each other and \(\vec{p}_{1} \left|\right| \vec{p}_{2}\). The force between the dipole is:
1. \(\frac{1}{4 π\varepsilon_{0}} \frac{4 p_{1} p_{2}}{x^{4}}\)
2. \(\frac{1}{4 π\varepsilon_{0}} \frac{3 p_{1} p_{2}}{x^{3}}\)
3. \(\frac{1}{4π\varepsilon_{0}} \frac{6 p_{1} p_{2}}{x^{4}}\)
4. \(\frac{1}{4 π\varepsilon_{0}} \frac{8 p_{1} p_{2}}{x^{4}}\)
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