Questions in electrostatics

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Two electric charges $12\mu C$ and $- 6\mu C$ are placed 20 cm apart in air. There will be a point P on the line joining these charges and outside the region between them, at which the electric potential is zero. The distance of P from $- 6\mu C$ charge is
In the given figure distance of the point from A where the electric field is zero is
Figures below show regular hexagons, with charges at the vertices. In which of the following cases the electric field at the centre is not zero
An electron is moving towards x-axis. An electric field is along y-direction then path of electron is
An electron enters in an electric field with its velocity in the direction of the electric lines of force. Then
An electron of mass $m$ and charge $e$ is accelerated from rest through a potential difference V in vacuum. The final speed of the electron will be
The radius of a soap bubble whose potential is 16V is doubled. The new potential of the bubble will be
The dimension of (1/2) ${\varepsilon _0}{E^2}({\varepsilon _0}$: permittivity of free space; $E$: electric field) is
In the rectangle, shown below, the two corners have charges ${q_1} = - 5\mu C$and ${q_2} = + 2.0\mu C$. The work done in moving a charge $+ 3.0\mu C$ from $B$ to $A$ is (take $1/4\pi {\varepsilon _0} = {10^{10}}N{\rm{ - }}{m^2}/{C^2}$)
A cube of a metal is given a positive charge Q. For the above system, which of the following statements is true

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