Two charges $-q$ and $+q$ are located at points $(0,0,-a)$ and $(0,0, a)$ respectively.

$(a)$ What is the electrostatic potential at the points $(0,0, z)$ and $(x, y, 0) ?$

$(b)$ Obtain the dependence of potential on the distance $r$ of a point from the origin when $r / a\,>\,>\,1$

$(c)$ How much work is done in moving a small test charge from the point $(5,0,0)$ to $(-7,0,0)$ along the $x$ -axis? Does the answer change if the path of the test charge between the same points is not along the $x$ -axis?

Three point charges $Q, 4Q $ and $16Q $ are placed on a straight line $9$ $cm$ long. Charges are placed in such a way that the system has minimum potential energy. Then

An electron (charge = $1.6 \times {10^{ – 19}}$ $coulomb$) is accelerated through a potential of $1,00,000$ $volts$. The energy required by the electron is

A problem of practical interest is to make a beam of electrons turn at $90^o$ corner. This can be done with the electric field present between the parallel plates as shown in the figure. An electron with kinetic energy $8.0 × 10^{-17}\ J$ enters through a small hole in the bottom plate. The strength of electric field that is needed if the electron is to emerge from an exit hole $1.0\ cm$ away from the entrance hole, traveling at right angles to its original direction is $y × 10^5\ N/C$ . The value of $y$ is

What is the potential energy of the equal positive point charges of $1\,\mu C$ each held $1\, m$ apart in air