Two charges $10 \mu C$ and $-10 \mu C$ are placed at points $A$ and $B$ separated by a distance of $10 \ cm$. Find the electric field at a point $P$ on the perpendicular bisector of $AB$,at a distance of $12 \ cm$ from its midpoint.

What is an electric dipole? What is an electric dipole moment?

Two point charges $-4 \mu C$ and $4 \mu C$,constituting an electric dipole,are placed at $(-9, 0, 0) \ cm$ and $(9, 0, 0) \ cm$ in a uniform electric field of strength $10^4 \ NC^{-1}$. The work done on the dipole in rotating it from the equilibrium position through $180^{\circ}$ is: (in $mJ$)

Two charges of $+25 \times 10^{-9} \, C$ and $-25 \times 10^{-9} \, C$ are placed $6 \, m$ apart. Find the ratio of the electric field intensity at a point $4 \, m$ from the center of the electric dipole on the $(i)$ axial line and $(ii)$ equatorial line.

An electric dipole with dipole moment $\vec{p} = \frac{p_0}{\sqrt{2}}(\hat{i}+\hat{j})$ is held fixed at the origin $O$ in the presence of a uniform electric field $\vec{E} = E_0 \hat{i}$. If the potential is constant on a circle of radius $R$ centered at the origin as shown in the figure,then the correct statement$(s)$ is/are:
($\varepsilon_0$ is the permittivity of free space,$R \gg$ dipole size)
$(1)$ $R = \left(\frac{p_0}{4 \pi \varepsilon_0 E_0}\right)^{1/3}$
$(2)$ The magnitude of the total electric field on any two points of the circle will be the same.
$(3)$ The total electric field at point $A$ is $\vec{E}_A = \sqrt{2} E_0(\hat{i}+\hat{j})$
$(4)$ The total electric field at point $B$ is $\vec{E}_B = 0$

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